Which method can be used to determine the pKa of an acid-base indicator like bromothymol blue? I have a question about how one would determine the pKa of an acid-base indicator such as bromothymol blue. 

I know that spectrophotometric analysis is one option, but is it possible to perform an acid-base titration to find the pKa (7.1)? How would one set up this experiment? 

I was thinking I would use a pH meter/titrant curve and treat the indicator like a weak base, but what titrant would I use? Would I use a strong acid like HCl?
Yes, HCl would work with a pH meter. If you know the mass of base (indicator) you use, you can as 0.5 equivalents of a strong acid such as HCl and determine the pH. At that point, since the weak base would be half protonated, the pH would be equal to the pKa, based on the Henderson-Hasselbalch equation. Or you could just so the whole titration and find the pKa halfway to the equivalence point.

In this case, you have to make sure you start with the basic form of the indicator, however. Not sure what form it is supplied in.