You can enable Curl using easyapache script of cPanel/WHM. However, sometimes you may require installing it manually. You will have to follow below steps in order to install it manually:

1. cd /usr/local/src
2. wget http://curl.haxx.se/download/curl-7.19.5.tar.gz
3. tar -xvzf curl-7.19.5.tar.gz
4. cd curl-7.19.5
5. ./configure –prefix=/usr/local –with-ssl=/usr/include/openssl
6. make
7. make install

Please make sure that this will install curl and also associate it with openssl.

Note: Do not forgot to restart apache once you finish above steps.

Thanks!