Clues integrating jcart in Drupal 7
You need to include the file itself, module_load_include can help you with that. Then you need to instantiate the class, you should read the docs about jcart to figure out how to do that, but something like

 $jcart = new jCart($args);


This can be done in your theme, or ever better create block in your module than will display the cart and that will invoke display_cart.

Note I don't know anything about jcart, and as such the code is just an illustration.