Is there a test that measures gender dysphoria?
Short answer
Yes.

Background
A cursory Google Scholar search with the key terms Gender Dysphoria Questionnaire brought up 


  The Gender Identity/Gender Dysphoria Questionnaire for Adolescents and
  Adults.


If you wish to search for more related inventories you can look further using keywords like 'gender dysphoria' + 'inventory' / 'test' / 'diagnosis'.

References
- Deogracias et al., J Sex Res (2007); 44(4): 370–9
- Sing et al., J Sex Res (2010); 47(1): 49-58