YouDao has an example of 我去洗把脸:
知道了,妈。我去洗把脸,让自己清醒一些。
Zhīdàole, mā. Wǒ qù xǐ bǎ liǎn, ràng zìjǐ qīngxǐng yīxiē.
I see, Mummy. I'm going to wash my face and wake myself up.
and I just encountered it in the Chinese TV series 如果蜗牛有爱情, with the English title When a Snail Falls in Love (Wikipedia), in the first episode on QQ about 15 minutes, 49 seconds in:
There's similar examples at YouDao for 洗把脸.
It seems weird to me to put 把 in 洗把脸. I would expect 我去洗脸 or 我洗脸去. YouDao indicates 我要去洗脸了 and 把脸洗 are good choices.
Question: Why is 把 in 我去洗把脸?
I see no real reason for 把 to be in there. My guess is that it's a variation on 把脸洗.