This was answered by Banana56, but to elaborate a little more, this isn't how IP rights usually work. As the IP holder for Street Fighter, anything directly-related with SF belongs to them. That would include Karin. She may have been designed by the manga artist, but that doesn't really matter, as this was still an officially-licensed Street Fighter manga, not an original work (which, 95% of the time would not be owned by the mangaka anyway, but rather their publisher). Regardless of the designer, as a Street Fighter character that appeared in official Street Fighter media, Capcom owns her and can use her however they want (which they have done several times over the years).
Rare's work on Donkey Kong Country is a good comparison. The Kremlings were original villains designed by Rare for that game, so one might think they stayed with Rare after the Microsoft buyout, but they eventually clarified that as DK villains in a DK game, they were tied to the DK IP and are therefore owned by Nintendo, not Rare.
IP rights are confusing, and there's always an exception to everything (the terms of a licensing deal could
specify that the designer retains use over original characters, for instance, or even that both the IP holder and designer are equally free to use them), but this is generally how it goes.
lol, sorry, I ended up rambling on a for a bit, didn't I?
