You can record an inbound call at Plivo in two ways
Using record API:
The Record API can record live calls at any time during the call and returns the URL of a file containing the audio recording.
For more details: https://www.plivo.com/docs/api/call/record/#record-a-call
To get the callUUID of the live call so as to record the inbound call, you can make use of these APIs
Using Record XML:
The Record XML can be used to record the inbound call by having the XML appended in the answer_URL of the application attached to the Plivo DID(Your Plivo phone number).
During an inbound call to the Plivo DID the answer_URL of the application attached to DID will be executed. The answer_URL should contain below XML.
<Record action="http://foo.com/get_recording/" startOnDialAnswer="true" redirect="false" />
For more details: https://www.plivo.com/docs/xml/record/#record-a-complete-call-session