Both are grammatically correct and either can be used, but should be in the past tense.

Google ngrams suggests that "I was born on Tuesday" is slightly more common.

Kwabena [is the] (soul-)name of a male born on a Tuesday.

Certainly one born on Tuesday could not do better than to unite with one born on Wednesday. Expect sparks to fly from this!

Both are grammatically correct and either can be used, but should be in the past tense.

Google ngrams suggests that both are used.

Kwabena [is the] (soul-)name of a male born on a Tuesday.

Certainly one born on Tuesday could not do better than to unite with one born on Wednesday. Expect sparks to fly from this!

With a specific date, don't use "a":

He was born on Tuesday the 2nd March 1852