I know that 父 means father and it's readed "chichi". I thought the other reading of it was "tou" since I've heard many times o tou san to refer to a father. But according to this list https://en.wikipedia.org/wiki/List_of_j%C5%8Dy%C5%8D_kanji the readings of 父 are "fu" and "chichi". Is that list incomplete or does tou of o-tou-san written with other kanji?
Yes that list on Wikipedia is incomplete. The article says:
The readings presented here are those noted in the official Jōyō table. 
And  refers to this official Joyo kanji list (PDF).
This PDF actually lists many special and/or jukujikun readings in the notes (備考) and the appendix, but those special readings are not included in the article on English Wikipedia.
What's written on the fourth (備考) column is omitted.
お父さん is a reading which is both very common and "official", but there are actually many other readings not listed in the official joyo kanji list. See this question.