Eloqua: How can we capture "First Marketing Channel" and append it to a new contact record?

Hello. We are in process of moving to Eloqua and need to understand how to capture a person's "First Marketing Channel" and include that on a contact record. For example, an unknown visitor finds our website via Google (an organic search). Then they submit a form on our site and become a known contact. How can we see that the person found our site via Google? Is it part of their "visitor record"? If so, how can a visitor record get connected the person's contact record after they submit the form?

Is this automatically done within Eloqua? Or do we need to set up an integration with Google Analytics? Any insight would be helpful.