I have a bike tire that’s 26x2.3 and I need a new tire would a 26x2.25 fit on the same rim ?

Chances are 99.999999% - YES! You're only talking 5/100th of an INCH. You could probably go a lot thinner than that too.

Good article from the late cycling guru, Sheldon Brown. https://www.sheldonbrown.com/tire-sizing.html

Yes, any rim that can take a 2.3” wide tire will also be able to take a 2.25” tire. The width difference is only in the widest part of the tread. The bead of the tire(contact point to the rim) will have the same width with almost all mountainbike tires regardless of tread width.

The 26” designation can be tricky, as it has 5 different sizes that aren��t compatible. It’s safer to go by the millimeter size, which should be 559 mm diameter for the most common 26”. If your diameter is indeed 559 mm, then that difference in width is nothing to worry about.