Add custom form to panels?
Create a custom module that defines a block with that form as the content. You can then place that block anywhere on your site using the standard Drupal interfaces (blocks configuration, Panels, Context, etc.).

There are many readily available resources on creating custom modules that define blocks. The Drupal.org Module Developer's guide is a great place to start, as well as the Examples module, which includes a sample module for defining blocks that can be easily copied and customized.