Technically the name of this question is a bit of a misnomer, as I'm not talking about just Velociraptor mongoliensis, but any dromaeosaur (or dromaeosaur-shaped creature I suppose). How would, hypothetically, a sapient velociraptor wear clothes in order to blend in with human society? Would they just wear things like ponchos? Could they put on pants?
The thermal jackets they use for birds that are recuperating after surgery might give you somewhere to start since the dromaeosaurs and avians share the same basis body plan. They're basically puffer jacket vests, very Marty McFly in fact. As for pants I'd suggest suspenders that wrap over the back rather than the shoulders as probably a must the rest is a matter of tailoring.
I think this is going to depend significantly on how long and/or flexible your raptors' arms are. Can they reach behind themselves, for instance? Can they touch the base of their tail? (In front? In back?)
I'm going to assume they can touch their shoulders and vent, but have very limited ability to reach behind themselves. I'm going to assume also they have some ability to extend their arms outward, because if not, they're going to have a hard time dressing themselves, period. (If they're more flexible, it will give you more options for how to put on and take off clothing.)
As noted, they probably don't need clothing, aside from pockets, and they'll probably want pockets on their chest and at their flanks.
For uppers, they might just wear shirts and/or vests, like us. I think they'd be able to pull a vest (or shirt that opens in front) over their arms and head. Another, easier-to-manage option would be something which is split at the sides; this can be easily pulled over the head and then the sides fastened together. Note that the back will likely be wider than the front and will wrap around the front partway.
For "pants", you can get a bit more creative. One thing, though; because of their tail, they are not going to be able to have pants with no complete split the way humans can. One option is to have a cuff that goes around the tail with material in front and back. Like above, the bit that goes over the back will be wider and will wrap around in front of the legs to attach to the other piece. The lower piece might have a fly or flap for, ahem, "sanitary purposes". Another option, if they can reach behind themselves, is to have something more like human pants that they can pull up their legs, but is completely split in back, sort of like a shirt but backward.
I would definitely encourage doing some research on animal clothing. If you're looking to cover "naughty bits" in particular, I would look into animal diapers (yes, diapers), since — most animals not being trained to dress and undress themselves and use toilets — other clothes are usually open in the relevant places. I would also particularly look at bird diapers. Yeah, they're a thing. You'll also find them often called "flight suits". The drawback of many of these designs, however, is that they generally aren't designed to be put on by the critter wearing them, and thus the closures are generally not in locations that would be convenient for the wearer.
(That said, it would make for an interesting story if your raptors don't or can't dress themselves, and have sla^Wassistants for that purpose... and either have to be undressed to relieve themselves, or wear clothing that also serves to collect and contain wastes. Of course, it would also be interesting if they just didn't care, but that would seem contrary to the premise of your question.)
p.s. On that note, for certain tasks, they might indeed have "clothes" that have a built-in provision for waste collection. (This seems to be a fairly prevalent feature of futuristic space suits, in particular.)
People have put clothing on chickens.
A quick image search of 'chickens wearing cloths' showed mostly head coverings and vests. Pants would be more reasonable with people/animals that avoid pooping in their pants.
Why do people wear clothes:
- Status as a person: a creature wearing cloths is much more likely to be a person then a naked creature.
- Societal status: bling or just pure large number of hours of work.
- Physical protection: cloth armor is very effective, used for thousands of years, still used in the form of kevlar today.
- Information hiding. A poker face is useful. Clothing makes a poker body easier.
- Group identification AKA uniforms.
- Group acceptance.
These will apply to any people including people that look like velociraptors. So they will wear clothing for those reasons and more.