Wired dives into the science and physics of drones to figure out this age old question. The short answer is yes, with enough rotor area a “drone” can generate enough force. For a standard drone size the power requirements to generate enough lift are too great. Please do not attempt.
Let’s focus on the rotor-based drones, though. Their key to lift is their rotors’ thrust: A rotor’s main job is to take air from above the aircraft and push it down at some speed. Let’s imagine that in some short time interval, the rotor takes a cylinder of air above (that was initially at rest) and gives it some final velocity moving down.
In the end, the total rotor area is very important. For a given drone weight, you could either make a larger rotor (or more rotors) and push the air down at a slow speed, or you could make a small rotor and push the air down at a fast speed.
The air starts from rest above the rotors but then has kinetic energy below. This energy depends on the mass and the velocity of the air.
Theoretically, a drone could lift any amount no matter what size rotor it has. But on a practical level, there are two limitations. First, the maximum air speed is probably around 40 m/s (based on my calculations for the physics of the S.H.I.E.L.D. Helicarrier). Second, if the drone had a power of something crazy like 1,000 Watts, it wouldn’t be able to fly very long.
I get a rotor radius of 0.188 meters for a total rotor area (6 rotors) of 0.67 m2. Assuming a total drone plus human mass of 70 kg I can first calculate the required thrust speed in order to hover. With these values I get 43 m/s—that seems plausible. Now for the power, I get 14.8 kilowatts (you can see my calculations here. A power of 14.8 kilowatts is sort of crazy high. A normal-sized house could probably get by with less than 3 kilowatts. Just saying.