Do you have a right to a Polygraph?

No. You have no right to have a polygraph test. However, you can set up your own polygraph test and invite the DA to send their representative to your polygraph and to use the results as they see fit. If they decline your invitation, you could still send them your results. Polygraph tests are generally inadmissible at trial. Understand that if you take your own test, its possible that if you pass the DA will the AGREE to give you their own polygraph, and if you pass it, that may be to your benefit.