Can you use cement to tile on an asphalt floor?

If you are positive that it is asphalt I would not suggest adhering tile directly to the asphalt. If removal of asphalt is not an option I would install a subfloor and use thinset mortar to adhere the tile. Another option (probably the better option) would be to pour a concrete mix over the asphalt. Than use thinset to install the tile. The concrete will incapsolate the asphalt. Asphalt more than likely has oils in it and can be a hazard.