You'd use the Custom Object REST API. Marketo REST APIs: Custom Objects » Marketo Developers
But I would advise a thorough evaluation of whether this is better done with SFDC objects or Marketo objects.
The best way to do this is to use the standard "Assets" objects in Salesforce and map it as a custom object in Marketo. by default, and asset in SFDC can be linked to an account and to a contact, so you will have to choose which of these 2 relationships you want to use when mapping it in Marketo. I usually use the account one, at least for B2B.
Thank you Sanford and Greg for the replies and the advice. It seems like this is something I should take up with our SFDC admin as you both suggest that it's better to start from the Salesforce side and then map to the Marketo object.
I appreciate your advice. Very helpful. Thank you both for taking the time to reply.