Yes, you can. Some people will insist that paella can only be made using a paella pan and with the exact right ingredients as those used by the traditional Valencians. The making of paella with an ordinary pan requires that you make some adjustments to the ingredients and the cooking times, though.
Ordinary pans are smaller than paella pans.  Therefore, you shouldn't overcrowd the pan. This will help you avoid making your rice lose texture. Remember that a great paella must have the essential basic ingredients such as saffron and round rice.