Yes, a curling iron works just as well as a straightening iron, but it takes longer and you have to do it in small sections at a time. It definitely gets the job done though. I've done it plenty of times. I just listened to music to get me through it. Try it right now on a small section of your hair and you'll see.
Use a good curling iron at a higher heat level than you usually do (but not too hot so you don't ruin or burn your hair). Smooth it down slowly then curl it in or out back to the top and hold it. Careful not to burn your hair though. If you're gonna use a product, it can be tricky to choose and it needs some experimentation till you find something that's light (a lotion, moisturizing spray, heat protector, etc.) so you don't lose body and it gives it some shine. Don't use a pomade or anything with vaseline in it because it'll ruin the results. Try Pantene Relaxed and Natural Daily Oil Cream Moisturizer, Neutrogena Triple Moisture Silk Touch Leave-In Cream or Frizz-Ease by John Frieda, but use very, very little of it. I use a 1 inch barrel curling iron size but I'm sure a 1.5-2 inch would make the process much quicker.
*** Edited: Here are a few links that might help you. The girls in the long hair care forum (first link) are really knowledgeable about all sorts of black hair care issues and are really supportive of one another. I think you might find it interesting to skim through the forum. Click on Forums, then Hair Care Tips and Product Review Discussion.