R.A.P. Music received widespread acclaim from music critics. At Metacritic, which assigns a weighted average rating out of 100 to reviews from mainstream critics, the album received an average score of 85, based on 27 reviews, which indicates "universal acclaim".
Among those who reviewed the album positively was Allmusic editor David Jeffries, who gave it four out of five stars and stated "rapper Killer Mike already had an incredibly strong discography before R.A.P. Music landed [...] Revolutionary stuff and absolutely no fluff, R.A.P. Music is outstanding." Evan Rytlewski of A.V. Club praised the album's production and Mike's politically charged lyrics and wrote "[R.A.P. Music] feels like the culmination of his unusual career."Pitchfork Media's Ian Cohen picked the album as the Best New Music giving it an 8.6 out of 10 rating noting that "even if R.A.P. Music doesn't break enough rules or have enough of a platform to reach the levels of Fear of a Black Planet or Straight Outta Compton or Death Certificate . . . it does come off as the kind of powerful mid-career album those acts should've been able to make as hip-hop's elder spokesmen". Christopher Weingarten of Spin gave the album 9 out of 10 and wrote "A child of the '80s and a student of the Internet, Killer Mike is as exciting and wildly unclassifiable as hip-hop gets: New York noise and country shit, nods to when rap was punk and crunk was pop, Ice Cube before he needed hooks, David Banner before he needed to whisper, and Willie D before he needed anybody."Sputnikmusic staff Sobhi Youssef gave the album five stars out of five and praised El-P's synth-bass-heavy production and Mike's lyricism, and noted the album as "a hip-hop masterpiece to be remembered for years to come".
In a less positive review, NME writer Henry Barnes gave the album a 5 out of 10, stating that "Mike has dabbled with politics in the past, and even made unlikely forays into experimental soul, but ‘RAP Music’ lacks the fury and vitality that usually sustains him. The ambition is to be applauded, but half the album’s a grind. And not the good kind."
Complex named the album the 32nd best of 2012. The album was listed at number 20 on Rolling Stone's list of the top 50 albums of 2012, saying "Ten-plus years into his career, Outkast colleague Killer Mike stepped up to headline status with a bare-knuckled, politicized Southern-rap record produced by New York sci-fi dystopian El-P."  The album was listed 23rd on Stereogum's list of top 50 albums of 2012. English magazine The Wire named the album the 27th best of 2012.