This app was mentioned in 4 comments, with an average of 4.50 upvotes
Telltale has quite a number of their games available on mobile. Android link, iOS link.
A few more titles worth checking out:
And a few classic adventure games are available as well, as /u/moonshinesalute mentioned, like:
Apart from those, there are games that look similar to choose-your-own-adventure books like Choice of the Deathless, but I'm not very familiar with those yet.
Hope this helps!