Yes you
can, but I got a
lot out of taking voice lessons for a little while. I was really terrible, starting totally from ground zero "can't carry a tune in a bucket." Lessons helped me figure out a direction, and helped me learn how to practice. I'm still not a great singer by any means, but now I can at least be
somewhat competent behind a mic (and more importantly, when writing).
Oddly, one thing that really helped my singing is having a kid - I sing along to every kids' tune and tv show theme song, most of which are major scale variations (Twinkle Twinkle, Itsy Bitsy Spider, etc). It really got that in my ear. My son also usually likes when I sing to him, so I get more practice.