There are lots of different types of game designers, and "game designer" can mean completely different things depending on which studio you're asking. It's certainly helpful for a game designer to have basic programming knowledge, and it's probably even required at some studios, but it's not like you can't possibly work as a game designer without knowing how to program.
I would recommend learning it on your own time though! Find a language that looks interesting, and work through some tutorials. It's actually lots of fun!