Is there a way that when contacts are created via API, How to associate Persona.
You should be able to associate a contact with a persona by updating the contact via this endpoint. Since "persona" is technically just a HubSpot property, you can make a POST request to that endpoint, using the internal value of Persona (hs_persona) as the property, with the value being whatever the internal name of one of your personas may be.
Otherwise, if you're asking about associating personas after a Contact has been created via the API, you should be able to do so via a Workflow in-app: https://knowledge.hubspot.com/contacts-user-guide-v2/how-to-assign-personas-to-your-contacts. Your enrollment criteria would be that the "original_source_drilldown_1" is "API".