The sentence should be:
"I rarely drink coffee in the morning."
After "I", we use the base form of the verb ("drink") in the present tense.
"Rarely" is an adverb of frequency, so the sentence follows the normal present tense structure.
The other options don't fit grammatically:
(A) drinks — used with he/she/it, not "I."
(B) drinking — is a gerund or present participle, doesn’t fit here.
(D) to drink — is an infinitive, not correct after "rarely."