What type of visa is required to be allowed to earn a PPL in the US?
For a foreigner to come to USA to learn to fly, one would need an F-1 or M-1 visa.

This article in Flying magazine provides some information. You can get more information on from this school1. Also, you can look at this meta question: Can I ask about details of coming to the US to get a PPL?

Update:

It appears that you are already in the US on H-1b visa (it wasn't mentioned in the question), you need to go through the security clearances mentioned in Alien Flight Student Program (official version on TSA website).

AOPA has put together the related information (website). I also found about this flight school1 which has outlined the process.

If you search on Google about Alien Flight Student Program, you will find a ton of information.



1: Disclaimer I am not advertising any flight school.