Although some weird Japanese phone makers did have smartphones with radiation detector built-in (SHARP 107sh and 205sh), I don't think it would be a popular feature.

There isn't so many cases in daily life that one can encounter a radioactive source. Even if you are actively looking for one (don't do it), you will have a hard time if you don't work with radioactive sources occupationally.

Also, it's not physically possible to create a small and yet sensitive radiation detector.