Rasool is from Bijbehara in Anantnag district of Kashmir, India. His coach there was Abdul Qayoom who has played first-class cricket for Jammu and Kashmir. Before playing junior cricket for Jammu and Kashmir, Rasool learned the game from Qayoom. Rasool's father, Ghulam Rasool, and brother, Asif Rasool, both have played competitive cricket.

During 2009 Champions League Twenty20, Rasool was detained by the police in Bangalore in connection with a suspected presence of traces of explosives in his bag. He objected to the checking of his bag by sniffer dogs at his hotel. After questioning, the police learned that his resistance was only due to the presence Quran and a prayer mat in the bag. Rasool had come to Bangalore as a part of the Jammu and Kashmir Under-22 team playing in the CK Nayudu Trophy, and was staying at the KSCA's residential complex which was a few yards away from the Chinnaswamy Stadium. Rasool was released by the police after a few hours as no incriminating evidence was found.

In the 2012–13 Ranji season, Rasool scored 594 runs from 7 matches at an average of 54 including two centuries, and took 33 wickets at an average of 18 with three five-wicket hauls. His impressive performance was rewarded as he was included in the India A squad to play the warm-up one-day match against England on 6 January 2013. With this, he became the first cricketer from the Kashmir Valley to be picked for India 'A'.

In February 2013, Rasool wreaked havoc in his three spells as he took 7 wickets which helped Board President's XI bowl out the visiting Australian side for a modest 241 and scored winning 36* runs. His seven scalps included top-order batsmen such as regular Test opener Ed Cowan, stand-in captain and wicketkeeper Matthew Wade and future Australian cricket captain Steve Smith.

In February 2013, Rasool became first cricketer from Jammu & Kashmir to bag an IPL contract, signing up with the Pune Warriors for the 2013 season. He made his IPL debut on 9 May 2013 against the Kolkata Knight Riders at Pune. He got the wicket of Jacques Kallis and finished with figures of 1/23 off 4 overs in that match. He played his next IPL match against the Mumbai Indians on 11 May in which he scored 4 not out and bowled one over conceding five runs.

In 2013–14 Ranji Trophy, Rasool scored 663 runs with two centuries and three half-centuries at an average of 51 and took 27 wickets with two 5 wicket hauls in 9 matches. Under Rasool's captaincy, Jammu and Kashmir made it to the quarterfinals that season for the first time since 2000.

He was bought by Sunrisers Hyderabad at the 2014 IPL auction for ?95 lakh (US$130,000). He played 3 matches in IPL 2014. In his first match of 2014 IPL he took the wicket of Yuvraj Singh and bowled his spell nicely to likes of Gayle, Kohli and de Villiers, restricting them to concede minimum runs.

He was awarded with Lala Amarnath award for best all-rounder in domestic circuit after his performance in the 2013-14 Ranji Trophy season.

During the 2016–17 Ranji Trophy, he scored 629 runs in