Both an individual and a corporation can have an RNC in DR. The tax implications are different and one would need understand the plusses and minuses before proceeding.
That said, all a foreigner needs is a valid passport and a valid address here in DR to obtain an RNC attached to his name. Go down to DGII main office and fill out the necessary forms.
Without saying, the requirements for a corporate RNC are very different. Most attorneys here can advise.