Hard to say. Svidler tells a story of playing a pawn odds game against some 2100 guy and he said it was so hard he felt like when the game was drawn that he'd achieved something. He said the art of playing at pawn odds may be lost in modern times.
Kauffman considered odds a bit, and reminds us that the amount (in rating) that the odds are worth depends on the rating of the person receiving the odds. For a new player it wouldn't be worth anything, but at IM level play, where white is worth about 40 rating points due to being half a tempo up (and gambit theory says 2-3 tempi is worth a pawn), he says a pawn is worth about 200 rating points.
Carlsen is of course much stronger than an IM, so it would be worth even more to Carlsen. Lets say Carlsen would be expected to draw a match against a 3200 player if he had pawn odds.
So to beat Carlsen consistently (I assume you're asking about winning consistently), you'd want to be a few 100 points higher than that. 3 out of 4 is 200 rating points, so about 3400.
Interestingly this is about what stockfish8 is rated (although computer ratings are not FIDE ratings).
What would be the ELO rating for a player that could beat anybody in the world with pawn odds?