Hello,
One possibility that presents with annular lesions on the penis is of lichen planus. Lichen planus is an inflammatory disease that affects the skin and the oral mucosa, and presents itself in the form of papules(flat spots) or rashes. Treatment is available only on prescription and consists mainly of steroids, retinoids, hydroquinone and phototherapy.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.