Yes, the English word (and the Portuguese cognate, periferia) does have a Latin etymology, via Late and Medieval Latin peripheria.

Now, the Latin word peripheria itself has a Greek etymology, from Greek periphereia. But both Portuguese and English get their word via Latin (and, in the English case, possibly also French, which also gets it from Latin, though sources differ on whether English got it from French or directly from Medieval Latin, and its plausibly not uniquely one or the other.)