We've had anti-gravity technology since the first hot air balloons successfully took flight. Any engine that gets you off the ground is an anti-gravity device.
The Anti-gravity you're referring to in the science-fiction movies and TV shows are still decades or longer from becoming a reality. The closest thing we have to propulsion with no moving parts is a device called [the lifer] AKA FEEP or Field Emission Electric Propulsion, AKA Ion Wind. However these devices are very small and light weight and typically cannot produce enough thrust unless you're using a nuclear power source like a nuclear battery AKA Tritium Battery, to my knowledge we have not been able to use Ion Wind technology to fly heavy pay loads, much less a human in flight. That would require a large, dense source of power and high energy output. The only source of energy that might meet that demand would be nuclear.
This is based on my own research.