Could be two possible things here, its trying to run through php with something like the curl_exec function or what it looks like here is that the app is actually trying to run the curl binary manually which should be at /usr/bin/curl.
So first thing to do is to verify you have curl installed:
rpm -qa | grep -i curl
It should show you something like "curl-7" with a bunch of revision numbers after that. If you don't have it installed use your package manager to install it.
yum install curl -y
If it shows as installed run:
ls -l /usr/bin/curl
Verify that it shows as readable & executable for the third set of permissions.