I'm about to buy a MTB, since we don't have cyclocrosses here in my country. I'd like to have a road dropbar, but can't spend money on a road shifter like tiagra sti. I know the mtb handlebars are thinner than the road handlebars. Is there a way to make, say, a deore shifter on a road drop handlebar?
I'd recommend trying out some bar end shifters. You can get indexed ones for a few different gearing combinations. There are some ultegra bar end shifters on amazon for around $75usd. However, you could probably score some used ones cheaper via ebay. These are like what come on the surly cross check in the stock configuration.
You could mount regular rapidfire shifters on the top center part of the drop bars. It might take some widening of the clamp to get it to work. There is a thread on MTBR about an experience like this.
This is an older question but since no answer is marked "accepted" I'll add another.
If you are asking if you can move your shifters and brake levers to a road bar with no other change the answer is no unless someone is making a drop bars with an MTB bar diameter (I don't know of any). Your question doesn't mention levers but I assume you want to move those too :-)
There are adapters, bar end and stem mount shifters and there are alternative brake levers but they all amount to an expense that will start to approach the solution you want to avoid. A simpler option might be to just choose an MTB with a flat bar and add Origin-8 drops.
You might try mounting them as close to the center of the bar as possible, where you can reach them easily with your hands on the top of the bar, or reach both of them easily with one hand off the bar. I know this sounds clunky, but my first multi-speed bike was a Schwinn Varsity that had the shifters on the stem, and it was less difficult to use than you might expect without trying it. True, you can't change gears when pumping hard, but if you expect to need to be able to, you probably wouldn't be switching to drop handlebar.
According to Sheldon Brown's handlebar dimension page, older steel drop bars have the same clamp and grip size measurements as most newer upright bars. You should be able to find an old pair of steel drops that will be able to fit your shifters.