Is the word delineate used properly in the sentence There is a delineate line that separates New Mexico and Texas?

No. The Word delineate is the verb form (to delineate: to establish a line or extent, to mark precisely).

The past participle "delineated" could be used as an adjective, but using it to describe a "line" is grammatically redundant.

An acceptable form could be There is a delineated border that separates New Mexico and Texas.