If i reject a relic, can i get it offered again in the same run?

Will you get offered the same relic immediately after refusing?

No. I can confirm that.

Is it possible to randomly re-encounter a refused relic during the same run?

Probably not.

Games like Slay the Spire (e.g. the Binding of Isaac is a good second example here) work based off of a seeded random number generator. The number seed (i.e. the sequence of randomized dice rolls) is often decided before the player begins the game, and thus the chosen random option (relics, map layout, ...) are all fixed from that point on. Therefore, all of the relics you will encounter will already be assigned before you've even been able to accept/refuse the relic the first time.

There are exceptions to this (e.g. RPG games are more likely to generate random loot when you open the chest, rather than when you create your character), but that's often due to considerations of dozens of hours of gameplay, you can't generate every option.
Slay the Spire is much simpler and can effectively decide every choice before you start playing, and it's often done (specifically so you can share a seed with others so they can play the exact same game as you).