Drop bars commonly come in 26 mm and 31.8 mm. MTB bars usually come in 25.4 mm. Often, you can put a 26mm bar in a 25.4 mm stem, depending on the design of the stem. If not, it's not a big deal to replace the stem. Alternately, there are road bars available with a 25.4 mm diameter.

What is a big deal is figuring out what to do with your brake levers and shifters. With drop bars you have to use road style shifters and brake levers. Road levers and MTB brakes don't work together so you may have to replace your brakes as well.

Unless you have a source for cheap parts and labor, replacing handlebars, stem, brakes, cabling, brake levers, and shifters could approach the cost of a good entry-level road bike.