Hello @Mack Carr and welcome to the Atlassian Community!
Yes, Both Jira Software and Jira Service Desk have extensive REST APIs. Take a look here:
Server: https://developer.atlassian.com/server/jira/platform/rest-apis/
Hope these are helpful. If this answers your question, please click the "Accept Answer" button next to this answer so others benefit from the "answered" flag in their search results. Cheers!
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