Can psycotherapy alone cure anhedonia?

Depends: Anhedonia means having trouble enjoying life. It may or may not be part of depression. Sometimes anhedonia can easily be treated with therapy. However, if part of a treatment resistant depression, it may also need to be addressed with medication.

Yes: Assuming it is a symptom of depression, then yes, psychotherapy alone should be effective. Research shows that psychotherapy alone (in the long run) is as or more effective than medication-- it is really the preferred 1st line treatment. But if you do not respond to psychotherapy (serious, regular, at least weekly sessions), don't rule out medication. Some people- not most, but some- need both.

Psychotherapy: Anhedonia is typically a component of depression, and yes, therapy alone can be very effective in treating depression. Usually a combination of meds and therapy together are optimal.