The constructed language Toki Pona is written with IPA symbols. This is a phonemic transcription that doesn't account for allophonic variation, but still, the letters can always be read according to their IPA values. According to Wikipedia, the language has over 100 speakers. Here is an estimate of relative differences of the number of speakers of several conlangs, including Toki Pona, based on LinkedIn profiles.
I haven't found any natural language that is written with IPA without exceptions, but there are a few that come pretty close, e.g. Hawaiian.