Your therapist can prescribe T if he or she is a MD, DO, NP, psychiatric nurse, PA, or anybody else who has prescribing privileges. Until recently, all of my talk therapy came from physicians at a teaching hospital. Not everybody sees regular psychologists or social workers or whatever.
However, I'd feel pretty uncomfortable about getting T from anybody but a general practitioner or internist or whatever. Endocrinologists are not easy to come by, so I'm not a fan of directing people to them. Something so basic and long-term shouldn't require a specialist.
I got all of my gender therapy (and letter) from a regular therapist, but she was somewhat involved with the queer community, which helped. I wish I had access to an actual gender therapist. I come here so much partly because my therapists just don't get gender issues so I tend not to talk about them.