Can I apply for an F1 Visa if my Bi1/B2 was denied

My B2 Tourist Visa was denied a year back in August 2019 and I got admission into a US University for Spring of 2021. I have a valid I20 from the university as well as funds. Will my F1 Visa application and approval be impacted since B2 was denied (more than a year ago).

Well, both are different visas. Technically, they should not have any relationship, so you should be fine.

They may question you why it was denied, you just need to state the facts.
Also, as always, there is no guarantee that you will get Visa stamping 100%, it is up to the discretion of the consular officer.

Be confident and do your work, you will be fine !