The rule you're thinking of is one of these two:

Excised letters get replaced with apostrophes: don't, bo'sun

Pluralized acronyms can get apostrophes, especially when it gets confusing as to whether the `s' is part of the acronym: CPU's, CRT's

I suppose you could make the case that it fits the first of those, but, I think, in our jargon, ``app'' is no longer an abbreviation. I don't think it really quite fits the connotation of that rule anyway. I think it has more to do with transcribed oral elisions.