There are two problems with measuring rationality, one of which is difficult but manageable, the other of which might be insurmountable. The first problem is that most conceivable tests of rationality require using information from other fields (such as finance, physics, or psychology), such that you can gain a considerable advantage on the test by studying things from that field which don't actually make you more rational. This can be solved with sufficient cleverness.

The second problem is that how rational someone is depends on how well they maintain it under stress. Pressure, fatigue, emotionally charged situations, alcohol, and/or deliberate manipulation, can make the best rationalists act completely insane. (About a year ago, I went on a reality television show, which was in a way like a series of rationality tests. I didn't do all that well, rationality-wise, but some people who should have known better did dramatically worse.)