Undrafted, Angelidis made his professional debut during the 2006–07 season playing in 24 games in the ECHL with the Florida Everblades, where he scored 10 goals and 18 points. He then joined the Albany River Rats and has played in 235 career American Hockey League games, with the River Rats. During that time he scored 42 goals and 85 points with 456 penalty minutes. In the 2008–09 AHL season Angelidis led the River Rats in penalty minutes with 142 and was also tied for fifth in goals with 15.
On August 3, 2010 he was signed as a free agent by the Tampa Bay Lightning. Angelidis scored his first NHL goal in his first NHL game, on January 24, 2012 against Curtis Sanford of the Columbus Blue Jackets.
On March 12, 2015, Angelidis was recalled by the Tampa Bay Lightning after the team suffered a series of injuries at forward. Prior to the recall, Angelidis appeared in 57 games with the Syracuse Crunch, notching 17 goals and 33 points. On March 20, 2015, the Tampa Bay Lightning announced that Angelidis had been reassigned to the Syracuse Crunch. During his three-game stint with the Lightning, he recorded 12 penalty minutes, and a pair of fighting majors against the Montreal Canadiens.
On June 30, 2015, the Lightning announced the re-signing of Angelidis to a one-year, two-way contract. Angelidis skated in three games with Tampa Bay last season, recording 12 penalty minutes. He also played in 64 games for the Syracuse Crunch in 2014-15, recording 20 goals and 38 points while serving as the team's captain. Angelidis was third on the team in goals and points, and lead the team with 138 penalty minutes. Angelidis has been serving as captain of the Crunch since the beginning of the 2012-13 season.
On January 5, 2016, having spent the majority of the season with the Crunch, Angelidis was named the captain of the 2016 AHL All Star Classic.
In the off-season, Angelidis left as a free agent after 6 seasons within the Lightning organization. Unable to secure a NHL deal, on August 8, 2016, Angelidis signed a one-year contract with the Stockton Heat of the AHL, an affiliate to the Calgary Flames. On October 18, 2016, the AHL announced that it had suspended Angelidis three games for an illegal check to the head of an opponent in a game vs. San Jose Barracuda. Limited to 49 games through injury, Angelidis registered 7 goals and 20 points in helping Stockton to a post-season berth.
On July 4, 2017, after spending the first 11 seasons of his professional career in North America, Angelidis signed his first contract abroad. He agreed to a one-year contract with Italian based, HC Bolzano, of the Austrian, EBEL.
His cousin, Jeff Angelidis (born 1977), also played professional hockey in both Europe and North America. His spouse is Lenna Angelidis.