"An incarnation" in the Hindu and Buddhist sense of the word refers to one divine who recurs in a series of bodily forms.

Small "o" orthodox Christianity holds that Christ became man when conceived by Mary, and importantly, has and will remain man in that same form, insofar as he was bodily resurrected and after the 40 days ascended into heaven (with his body). When he returns again at the end of days, it will be in the same body.

So, it would be reasonable, and you could doubtless find theological writing, which refers to Mary's conception of Christ as his (one time only) incarnation, but meant quite differently from the Hindu / Buddhist sense.

The Incarnation (with a capital i) is a very common way to refer to Christ's birth by theologians. An early example would be St. Athanasius, who wrote a fairly short work appropriately enough entitled On the Incarnation. However, to say "an incarnation" of God would be seen as heterodox by virtually all Christians, since it implies that other incarnations may have occurred.