It is biblically forbidden1 to wear shatnez (mixture of wool and linen) even temporarily, and even if the garment does not belong to you.
You should have your rented tuxedo checked for shatnez even if you will only be wearing it once.
Click here for more about shatnez.
Best wishes,
Rabbi Baruch S. Davidson
Very helpful! We are so blessed that Hashem gives us His Torah and mitzvot! Thank you so much and Moshiach now :) Will use this advice for my upcoming wedding, G-d willing!