Quite the opposite really. English borrowed it from Welsh or Cornish (But most probably Welsh). Compare English "Father" (Germanic) to German "Vater" and Norwegian "Far", and English "Dad" (Celtic) to Welsh "Tad" and Cornish "Tas".
Thanks for the reply guys! Awh that's really cool, I love finding celtic/ brythonic words in English, I'm glad this one is in such common use!
According to Geiriadur Prifysgol Cymru there are very similar words in the old Indo-European, Latin, Greek, and Sanskrit, so it is probably one of those words, like 'tea'/te, that goes back a very long way and is common to very many languages.