*rubs my chaotic little hands together*
I just think they'd be really hot together okay! Sirius deserves a hot young boytoy after all those years in Azkaban!
Okay, but seriously, they're both brilliant men, the top of their respective classes at school. Both are outcasts in their families. I do think there's a bit of rebelliousness in Percy? In the sense that he could have just caved and been exactly the type of son/brother his family wanted and they would have stopped making fun of him, but he refused to do that, just like Sirius refused to bend to his own family's will.
I actually feel really bad for Percy now as an adult, like, his family was awful to him! Not just his siblings, but his parents too! No wonder he wanted out! And all for the crime of *checks notes* liking to follow the rules.
There's a great Percy defense essay that circulates here once in a while that outlines all this, but yeah, his family treats him like crap and Sirius knows what that feels like!
Also, as someone else pointed out, they've both got the whole Scabbers thing in common. Imagine an OOTP AU where Percy is at Grimmauld with the rest of the family and Sirius saunters up one day and is like, "Sorry my former friend pretended to be your pet for your entire childhood, that must be rough, want some Firewhiskey?" and Percy says yes to everyone's shock (including his own) and anyway I think they would bond after that.
Or imagine a universe where Sirius gets his freedom and he's at the Ministry a lot after that (maybe as Lord Black taking his seat on the Wizengamot, maybe just to cause trouble because he can) and he gets to know the Minister's assistant quite well. ;)
Also, they both have the Ministry screwing them over in common! Sirius's is obvious, but Percy got in trouble in GOF because he *checks notes again* did what his boss told him to do, and then the Ministry reprimanded him for it because he didn't realize something was up with Crouch?????
God, they would both hate Crouch and Peter sooooooooooooo much.
I think it would also be fun to watch Sirius loosen Percy up a bit, and I think Percy deserves a rich hot older boyfriend to take care of him.