If you have the premium feature for Payment Requests (Sites and Platform Edition) you will have access to the Payment Request feature. A Payment Request is a record that gets created and contains a link to a Visualforce page. This link can be sent to your customers email and allows them to process their credit card payment without human intervention.
You can automatically create a Payment Request record when a new Chargent Order gets created. If you go under the Chargent Settings tab > Advanced Settings, you will see a checkbox to Automatically Create PR Record. Your Salesforce developer can then create a Process that will allow the Payment Request to be sent to the Billing Email Address on the Chargent Order.
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