Born in Negotin, he started training when he was 7 years old, with his father Saša, who is also a former goalkeeper of Hajduk Veljko. He was with his hometown club until 2009, when he moved to Jagodina. For next 4 years, he played for youth teams of Jagodina, and was with first team since 2011–12 season, and was licensed with jersey number 45. For new season, Bondžulić changed his squad number to 11 again, so Rajković took 1. Although Bondžulić was the first choice, Rajković mainly was his reserve in front of competitors Petar Jokić and Stevica Zdravković. He made his professional debut for Jagodina on 9 March 2013, in Serbian SuperLiga match versus Partizan. Until the end of 2012–13 season, he made one more match against Smederevo. After Bondžulić's departure, Anđelko Đuričić joined to Jagodina. After first fixture and lost of Napredak Kruševac, Mladen Dodić decided to give a chanse to Rajković as a first choice, because of his merits in winning 2013 UEFA European Under-19 Championship. But, after 2 appearances in new season, Rajković left to Red Star Belgrade. Jagodina should receive 30 percent of his next transfer.
He signed a four-year contract with Red Star Belgrade on 28 August 2013, and took the jersey number 95, according to year of his birth. He mostly was a reserve of Boban Bajković, and fought for a place on the bench with Miloš Vesić. He made his official debut for Red Star in last fixture against Vojvodina.
After Bajković's and Vesić's departures, Rajković stayed with a year younger Filip Manojlović and Marko Trkulja who returned from Spartak Subotica, where he was on loan. Club management decided to sign more experienced goalkeeper, and Damir Kahriman signed with Red Star. But because of administrative problems he could not perform at the beginning of season, so Rajković started season as a first choice. After Milijaš's departure, Mijailović's suspension, Luković's injury, and Lazović's conflict with management, coach Nenad Lalatović decided to give the captain's armband to Rajković. He had 16 clean sheets on 28 league appearances, and was selected as the best goalkeeper in 2014–15 season, by the players choice.
On 29 June 2015, Rajković signed a new three-year contract with Red Star, after days of speculation about his potential transfer away from the club. After winning 2015 FIFA U-20 World Cup in New Zealand and the award for the best goalkeeper of the tournament, many European clubs wanted Rajković, including French Ligue 1 club Lyon, Belgian side Club Brugge and according to some reports Italian giant Serie A club A.C. Milan. Crvena zvezda captain was also a top target for Paris Saint Germain along with Kevin Trapp, who signed for Les Parisiens at the end. Rajković was the best member in team during both matches against Kairat in first qualifying round for the Europa League. Rajković kept team from suffering a harder loss with some incredible saves. The coach of Kairat, Vladimír Weiss, after the game said that Rajković is one of the best goalkeepers in Europe. After great saves in first rounds of the Serbian SuperLiga, despite Zvezda's poor start, Turkish champion Galatasaray declare interest for him and willing to offer 4 million euros.
Predrag Rajković was one of the contestants at 2018 FIFA World Cup qualifying draw, which took place at the Konstantinovsky Palace in Strelna, Saint Petersburg on 25 July 2015.
On 29 August 2015, Rajković signed a five-year contract with Maccabi Tel Aviv. The transfer fee was €3 million. On 30 August, Rajković made his Israeli Premier League debut in a 1–0 victory over Hapoel Be'er Sheva during the second league match of the season. Rajković made 43 appearances in all competitions, including Israeli Premier League, State Cup, Toto Cup in which he did not play and UEFA Champions League. He noted 21 clean sheets at total until the end of 2015–16 season. Rajković also continued playing as the first choice goalkeeper in the 2016–17 Israeli Premier League season. During the first half-season, he also made 14 appearances in the UEFA Europa League, which the club ended at third place in group stage. Rajković made an assist to Viðar Örn Kjartansson in the State Cup match against Hapoel Bnei Lod played on 7 January 2017, saving a goal in previous attack of opponent team.
Rajković was a member of Serbia U-16 and Serbia U-17 national teams. Rajković was one of the most deserving players for winning 2013 UEFA European Under-19 Championship, when he saved goal many times with the great interventions, and stopped penalties. Next year, he also was one of the best, but Serbia lost against Portugal in semi-final, after penalties. Rajković lead the team on 2015 FIFA U-20 World Cup, with the captain's armband. After group stage and first place, Serbia won Hungary after the extra time. In quarter-final, Rajković saved 2 penalties, and missed one in penalty series against USA. After Maksimović's goal, Serbia won for the next round. In the final, Rajković was one of the most important man on the field, keeping the result with incredible saves. Captain of Serbia national under-20 football team won nomination for the best goalkeeper on the competition. Radovan Ćurčić, coach of Serbia U-21 called him for friendly match against Israel, played on 6 February 2013.
Rajković was called in Serbia national football team under coach Siniša Mihajlović. He debuted in the senior team on 7 August 2013 against Colombia.As of 8 February 2017
As of 21 November 2016
Serbian Cup: 2013
Serbian SuperLiga (2): 2013–14, 2015–16
UEFA European U-19 Championship: 2013
FIFA U-20 World Cup: 2015
The Best Young Athlete of Serbia: 2013
2013 UEFA European Under-19 Championship: Team of the Tournament
FIFA U-20 World Cup Best goalkeeper: 2015