Scrivens played four years with the Cornell Big Red of the ECAC. After his senior season, Scrivens was named a first team All-American, ECAC Goaltender of the Year and was one of ten finalists for the Hobey Baker Award. He started his professional career with the Reading Royals of the ECHL, before being called up to join the Toronto Marlies at the end of the 2010–11 AHL season.
Scrivens played in the Alberta Junior Hockey League (AJHL) for two seasons. He broke into the league with the Drayton Valley Thunder during the 2004–05 season, playing a single game with the team before moving on to the Calgary Canucks. During his final year of junior hockey, Scrivens played with the Spruce Grove Saints. He won 27 games, while losing 12 and tying three, finishing the year with a 2.43 goals against average (GAA) and .921 save percentage. He was named the Saints' Most Valuable Player and Player of the Year for the 2005–06 season. Scrivens played in the AJHL All-Star game, and represented Team North at the 2006 Viking Cup, where they won the championship.
Scrivens joined the Cornell Big Red for the 2006–07 season. He played in 12 games, starting eight and recording three wins. He recorded his first collegiate shutout in a 6–0 win against Union College. During his sophomore season at Cornell, Scrivens established himself as the team's starting goaltender, playing in 35 of the team's 36 games. For the week of December 3, 2007, Scrivens was named the ECAC Hockey goaltender of the week. He was an honorable mention All-Ivy League after the season. He won 19 games, and finished with a 2.30 GAA and .911 save percentage. Scrivens retained his starting job with the Big Red during his junior season, and joined the ranks of top NCAA goalies across the country. He played in 36 games with the Big Red, recording 22 wins, a GAA of 1.81 and a .931 save percentage. Scrivens picked up many awards for his playing during the 2008–09 season, including being named the National Player of the Week for the first week of the season, as well as second team All-ECAC and an honorable mention All-Ivy League at the end of the season.
Scrivens' senior season with the Big Red saw him earn First Team All-American honors, while playing in 34 games and winning 21. He had a 1.87 GAA and a .934 save percentage. Scrivens captured the Ken Dryden Trophy as ECAC goaltender of the year, and was named one of ten finalists for the Hobey Baker Award. He finished his collegiate career with 19 shutouts, fourth all-time in NCAA history.
After completing his collegiate career, Scrivens had not been selected in the National Hockey League (NHL) Entry Draft, making him an unrestricted free agent, able to sign with any team in the league. The Toronto Maple Leafs signed Scrivens to a one-year contract on April 28, 2010. Scrivens' decision to sign with the Leafs was largely due to the presence of goaltending coach François Allaire, whom Scrivens had worked with during an off-season goalie camp.
Scrivens started the 2010–11 season with the Reading Royals of the ECHL, the Maple Leafs' second tier affiliate. He played in 13 games with the Royals, winning 10. For his efforts he was selected to represent the Royals in the ECHL All-Star Classic. His strong play at the ECHL level, and injuries to other goalies in the Maple Leafs systems, earned Scrivens two separate callups to the Toronto Marlies of the American Hockey League (AHL), one in November and one in February. Scrivens was one of two goalies on the Marlies Clear Day roster announced on March 8, 2011, meaning he would be spending the remainder of the season at the AHL level, barring injury or suspension.
The Maple Leafs re-signed Scrivens on July 1, 2011. He was called up to the NHL as of October 24, 2011, in an emergency situation. After serving as backup for the previous games, he made his first regular season start on November 3, 2011, in Columbus against the Blue Jackets. In that game, he recorded his first career win and stopped 38 shots in a 4–1 game. As the NHL resumed play after the 2012–13 NHL lockout, Scrivens became a full-time NHL goaltender for the first time, serving as the backup to James Reimer, starting Toronto's first two games. Scrivens recorded his first NHL career shutout February 16, 2013, in a 3–0 victory over the Ottawa Senators.
Scrivens was traded to the Los Angeles Kings in June 2013 along with Matt Frattin and a second round pick in exchange for goaltender Jonathan Bernier. Scrivens served as the backup goaltender to Jonathan Quick.
On November 12 of the 2013–14 season, Scrivens stepped in for Kings starting goaltender Jonathan Quick after Quick suffered a lower body injury with 1:20 remaining in overtime against the Buffalo Sabres. Scrivens then started the next three games, posting 23 saves in a 3–2 comeback victory over the New York Islanders on November 14 and recording consecutive shutouts against the New Jersey Devils on November 15 (with 26 saves) and the New York Rangers on November 17 (with 37 saves). Shortly after Quick's return in January, however, Scrivens became expendable due to the play of third goaltender Martin Jones, and he was subsequently traded to the Edmonton Oilers.
On January 29, 2014, Scrivens set the NHL record for most saves by a goaltender in a regular season shutout, stopping 59 shots from the San Jose Sharks during 60 minutes of regulation time, leading the Oilers to a 3–0 victory. Scrivens also set an Oilers franchise record in the process for most saves in a game, surpassing the previous record of 56 set by Bill Ranford in 1993.
The Oilers re-signed Scrivens to a two-year contract worth $2.3 million per season on March 3, 2014.
On December 28, 2015, the Montreal Canadiens announced that they had acquired Scrivens from the Edmonton Oilers, in exchange for forward Zack Kassian.
On July 14, 2016, Scrivens agreed to a one-year contract with HC Dinamo Minsk of the Kontinental Hockey League (KHL).
Scrivens was invited and accepted to play for Team Canada at the 2014 World Championships. In his international tournament debut, he finished as Canada's starting goaltender in the quarter-final loss to Finland. Canada finished the tournament in fifth place.
Scrivens is from Spruce Grove, Alberta. He is the middle child of Wayne and Dawna Scrivens, with an older brother, Adam, and a younger sister, Bronwyn. While playing hockey at Cornell, Scrivens studied Hotel Administration. He is married to Jenny Scrivens, since June 2012, also a professional goaltender currently signed to the New York Riveters. He and his wife are currently residing in Edmonton Alberta.