Yes, we can integrate shopping cart and payment processing applications into your website.
On my own SnapSizzleBop web site I use PayPal for payment processing. (Note: PayPal supports credit card payments from all visitors regardless as to whether or not the individual shopper has his or her own PayPal account.) PayPal also supports a shopping cart to purchase multiple items in one visit.
If you need a full inventory management system to handle multiple products, their availability, shipping info and more, shopping cart applications (such as Zen Cart) can also be integrated. These models require you to input extensive inventory data of effective use.