This tech doc details the xml payload on how to use Service Desk soap web service API methods for this task.
Release : 17.1/17.2/17.3
Component : SERVICE DESK MANAGER
You could use transfer() SOAP web service method. Detail of this method is documented here
https://techdocs.broadcom.com/us/en/ca-enterprise-software/business-management/ca-service-management/17-3/reference/ca-service-desk-manager-reference-commands/technical-reference/web-services-methods.html
for example, this payload from soapui will transfer the ticket to a new group
<soapenv:Envelope xmlns:soapenv="http://schemas.xmlsoap.org/soap/envelope/" xmlns:ser="http://www.ca.com/UnicenterServicePlus/ServiceDesk">
<soapenv:Header/>
<soapenv:Body>
<ser:transfer>
<sid>37469229</sid>
<creator>cnt:140557EBDC688E438487725370F1D7EA</creator>
<objectHandle>cr:400751</objectHandle>
<description>this is the description of api transfer</description>
<setAssignee>0</setAssignee>
<newAssigneeHandle></newAssigneeHandle>
<setGroup>1</setGroup>
<newGroupHandle>cnt:635361D30CDA43418202D895431764E0</newGroupHandle>
<setOrganization>0</setOrganization>
<newOrganizationHandle></newOrganizationHandle>
</ser:transfer>
</soapenv:Body>
</soapenv:Envelope>
Please notice that you could encounter some error if the existing assignee is NOT a member of the new group, if the option group_assignee_independent is not installed