No, curl isn't a part of php it is a GNU utility. PHP has a php-curl module though.
As for installation you probably don't want to install from source in general -- package management is pretty vastly superior these days. Not that you need to -- it is on macs by default, or at least was on the one I had handy with mavericks running on it.
All that said, if you want a command line http client I would use httpie -- https://github.com/jkbr/httpie, it is vastly superior.