I'm assuming you are on a Mac. This is a simple issue to fix.
First install Xcode. Then restart your computer. Afterwards run the commands in sequence,
xcode-select --install
brew remove portaudio
brew install portaudio
pip3 install pyaudio
So to clarify, Xcode is installed through the App Store. Xcode command line tools are required for some installations, for others they are not. I'm including it here just to be on the safe side. You also probably do not need to uninstall and reinstall the formula via Homebrew, I did that to ensure that there would be absolutely no problems.
Edit: I have been told Homebrew requires Xcode. So just run the
xcode-select --install
command to be able to use Clang. Also what version of Mac are you on?
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