I don't think there is a role. I think you need to determine the responsibilities and motivations a person might have for sponsoring and speak to their needs related to it. In my experience, the people with these interests in a company don't reside in just one role.
If they do have a person, then it would likely be someone tied to CSR (Corporate Social Responsibility). The best way to find this person is to see if the company currently sponsors other organizations and contact those people to find out who the key contact is.
I always look for the artifact that the organization is interested in doing something, then follow the trail backwards till you find the lead individual.
Generally sponsorships happen because a person(s) have a personal relationship with someone or they identify that the group will have a good impact on their business in exchange for their sponsorship.
Sponsorships can be done in many different ways...so get creative and you will be surprised how many companies will want to get involved. I have done this many times with non-profits or even for profits and we created a platform to get their brand out and had to start turning away sponsorships.