Yes. You can obtain a UAE Residence visa in exchange for real estate investment in the UAE. It is valid for 2 or 10 years. The minimum investment is AED 750,000, or approximately $204,000. With this visa, you can live in Dubai or in any other Emirate.
The Emirati government also introduced the new UAE Golden Visa program that grants residency permits for 2 and 10 years by investment or exceptional merit.