There are multiple ways to accomplish this, with both XmlRpc as well as Rest.
Rest methods: Keap REST API
XmlRpc invoice methods: xml-rpc - Keap Developer Portal
XmlRpc place order method: xml-rpc - Keap Developer Portal
Each of these have various positives and negatives. The XmlRpc place order method is the best option if you are looking to do as much in as little API calls possible, but again it comes down to what your integration needs are.
If you could provide us with as much detail around your desired integration and flow of data, we can provide a more specific answer suited to your use case.
Here are some of the questions that would help me to provide a more specific answer for you:
- Do you need to handle processing payments within Keap, or just looking to mark an order as having been paid?
- What other order related data needs to be generated or represented? Products, Promo codes, discounts, shipping costs, taxes, etc.
- Do you have recurring orders aka subscriptions, and how would you like those represented within Keap?
- Is this a one way sync, or will you be generating orders within Keap that you also would like sync’d back outward to other systems?