You mean a spindle? Of course you can! :D
A lot of people hate them, and those people are very, very vocal about hating them, in my experience.
I love them, and here's my take: if you are really determined, you can work through the frustration. Every new craft has that awful frustrating beginning, and if you can roll with it and keep going, you will catch on.
Personally I was very determined to spindle spin because I didn't see how there was any way that I could afford to purchase a wheel in the foreseeable future. So I knew if I was going to be a spinner, I was going to be a spindle spinner. (Of course the rest of my story is that I fell so in love with spinning that I raised the $$ to buy my wheel by spinning gobs and gobs of yarn...we're talking thousands of yards...and most of it was spindled!)
I don't know what your LYS carries...I'd recommend a spindle that weighs around 2oz. for a beginner though. Check out this board -- there are quite a few posts about tips for new spindle spinners. :D