"They" can be singular.
"This use of they isn't ungrammatical, it isn't a mistake, it's a feature of ordinary English syntax that for some reason attracts the ire of particularly puristic pusillanimous pontificators, and we don't buy what they're selling."
There's not a man I meet but doth salute me
As if I were their well-acquainted friend
- A Comedy of Errors, Act IV, Scene 3