Yes, sing. Join a choir, or theator. Even if you only have spoken parts you will learn to improve your voice in ways that translate to singing. Most churchs have a choir, if you attend one (even if only chrismas and easter) join the choir, and sing in it every sunday. Singing in a group is fun, even if you don't otherwise like the music.

Beware of overdoing it though. You want to improve your voice, not lose it or devolpe nodes.

Finially depending on what you want to sing consider investing in a good microphone and speaker system. Some songs need projection at soft volumns, and those who try to force their voice to do it lose the song. If your voice is natuarlly soft you may have to do this anyway.