As of February 2015, Shaiman lived in Dubai with his wife and children, working as an administrative executive at a petroleum storage terminal in Al Quoz. His younger brother, Arsalan Anwar, also played at first-class level for Sialkot, but retired early to concentrate on his career.
Born in Sialkot, Shaiman made his debut for Sialkot in March 2002, during the 2001–02 season of the One-Day National Tournament. He made his first-class debut during the following season of the Quaid-i-Azam Trophy, and in his third match, against the Lahore Whites, scored a maiden century. Opening the batting with Usman Mushtaq, Shaiman scored 106 runs from 118 balls, putting on a 177-run opening stand. Later in the season, against Faisalabad in the limited-overs competition, he scored 96 from 91 balls, and was named man of the match. Despite his good form during the 2002–03 season, in the next season Shaiman played only at lower grades. However, he did play a single Twenty20 match for the Sialkot Stallions in the ABN-AMRO Twenty-20 Cup during the inaugural 2004–05 season, as well as one Patron's Trophy match for Servis Industries during the 2005–06 season.
Having previously played club cricket, Shaiman moved permanently to the UAE in 2007, after gaining employment with a shipping firm. His first matches for Emirati representative sides came during the 2009–10 season, when he played for United Arab Emirates A against Pakistan A and the England Lions. After meeting the qualification requirements, Shaiman made his senior debut for the UAE national team in the final of the 2009–10 ICC Intercontinental Shield, which the team lost to Namibia. Shaiman has since been a regular for the UAE, and across the 2011–13 WCL Championship, scored 625 runs from 14 matches, the most of any player.
He made his One Day International (ODI) debut in February 2014, against Scotland in the final of the World Cup Qualifier, and his Twenty20 International (T20I) debut in March 2014, against the Netherlands in the World Twenty20. Shaiman was selected in the Emirati squad for the 2015 World Cup, and in the team's first match, against Zimbabwe, topscored with 67 from 50 balls. In the next match, against Ireland, he scored 106 from 83 balls, becoming the second UAE player to hit an ODI century (after Khurram Khan) and the first to do so in a World Cup.
In the 2015 ICC Cricket World Cup clash v Ireland,he along with Amjad Javed set the highest ever World Cup record partnership of 107 runs for the 7th wicket. In fact,this pair of batsmen became the first pair to have had a 100+ runstand for the 7th wicket in World Cup history.
On 14 April 2017, he became the first player for the United Arab Emirates to score a century in a T20I match, when did so against Papua New Guinea at the Sheikh Zayed Cricket Stadium, Abu Dhabi. Anwar also became the first UAE player to score centuries in both ODIs and T20Is.
He also holds the record for facing the most number of balls in a T20I innings when batting at number three position(68)