Yeah there is actually. IVM lets you control the software functions using the command line. You can read about the full SDK here, but the basic idea is:
executing ivm.exe -outbound 5551234 will make IVM dial out to 5551234 and play a pre-defined message (that could even contain variables like the person's name/num etc).
If you're using PHP for your website's code, it has a function to execute external programs with parameters (assuming your webserver and IVM are on the same PC) and you can use that to control IVM. If both are not on the same pc, you can install PHP on your IVM computer and then have your website send a request for a php page on the IVM PC which is programmed to execute IVM and call you.
Not sure if you understood all that, I don't really know what your level of programming knowledge/experience is, so let me know if you don't understand.