Would it have two, because it's technically two phonemes, or one?
Short answer: one (probably).
The definition of "morae" tends to depend on the specifics of the language and your analysis. They're not something we can necessarily measure quantitatively—instead, they're theoretical constructs used to make an analysis look nicer. (Sometimes morae do map cleanly to measurable units of time, other times they don't, sometimes linguists can't agree if "morae" are actually useful in analyzing a particular language's phonology or not.)
However, when you choose to call
[tʃ] an "affricate" instead of a "consonant cluster", that generally means you're treating it as a single phoneme. And you generally wouldn't do that unless it acts like one unit, not two, in your analysis.
So if you decide to call
[tʃ] an affricate
/t͡ʃ/ instead of a sequence
/tʃ/, it's probably because it functions as a single unit in your analysis, so it probably takes up a single mora. But this is a tendency, not a hard and fast rule.
Shorter answer: as many as any other single consonant. Coda consonants aren't necessarily moraic – in some languages they are, in some they are not. Affricates are usually single consonants with a particular kind of release (not everything written "ts, tʃ" is an affricate, sometimes they are sequences. "Affricates" are single sounds, not sequences of sounds). If a language has the rule Weight By Position according to which coda consonants are moraic, then affricates (not clusters) are moraic (mono-moraic).