Is it possible to use wpmember (http://wordpress.org/plugins/wp-members/) plugin integrate payment method using Infusionsoft payment gateway?
How to use Infusionsoft payment gateway in wordpress?
There are various plugins you can use with wordpress such as iMember360. This will give access to users who have purchased from you in Infusionsoft.
If you are looking to charge users on your wordpress site instead of using the infusionsoft shopping cart you can try Payment Gateway for WooCommerce
If you are interested in programming it yourself you can use the Order Service to create an order in PHP from a custom module/plugin you create.