It would depend on what you are referring to as sponsorship.
You can sponsor anyone in terms of completing the affidavit of support to meet the poverty guideline.
As far as petitioning for a non-relative, no but you can invite a non-relative to visit you and maybe employment sponsorship can also be attained for a non-relative.
I hope this addresses your concerns.
It is advisable to contact an immigration lawyer to address any other concerns you may have.
You are welcome to use the link provided.
The general answer to your question is no. In cases of immigration family law you generally have to be related, be it parent, spouse, child or sibling. So if the person you wish to sponsor has an immediate relative in the United States who is either a United States citizen or a green card holder they can sponsor someone abroad.
The other option for coming to the United States is usually a tourist visa which would allow the foreign national to come to the US for a period of up to 6 months. It is best to consult an attorney to help someone file the paperwork for a tourist visa.