They said that they purposely kept Raj single because it was realistic to his storyline. “Because of the way this finale was presented by Steve Holland, we didn't feel like it was necessary to have some big story closure for every character,” Lorre explained. ... So Raj's story just remains open.”

Why didnt they give Raj a girlfriend?

Raj reveals that he once had a girlfriend, after Leonard claims that the two of them were the only ones without them. He states that she was deaf, so his inability to speak with women was not an issue.

Does Raj end up alone?

Though Raj did end up alone in The Big Bang Theory finale (despite scoring a date with Sara Michelle Gellar), there were many characters who Raj could have ended up with.