Technically yes, Distinct was a verb but even by Noah Webster's time in 1828 it had fallen into disuse. I would suggest using the words Discern, Distinguish or Discriminate instead.
Which word you use is mostly a matter of preference but Discern implies the use of sight and Discriminate has picked up some negative connotations regarding stubbornly elitist attitudes. Discriminate has the benefit of a noun form (discrimination) without the visionary implications of discernment. It also sounds closer to distinct than distinguish.
In more recent times Differentiate has also become acceptable, probably to replace discriminate since English speakers often dislike repetitive use of words.
Do not use Determine for this exact purpose. Its closest definitions mean to give form to something or to Ascertain (make certain) which is a somewhat different concept. Proper discrimination may determine the distinctness of one thing from another but determination can not distinguish between the two.
Noah Webster's American Dictionary of The English Language (1828)
Webster's Revised Unabridged Dictionary (1913) [Cited just For differentiate.]