If all parts of your body are accelerated uniformly, as it happens in the gravitational field(caveat: far away from the source), then no, you can't.
Human beings perceive linear acceleration mostly via the otholitic organ in the inner ear. In it, suspended in viscous fluid are small crystals. Since the crystals are not rigidly connected to the rest of the body, whenever your head experiences acceleration they lag behind the bulk of your tissues due to inertia. Their displacement bends the tiny hairs lining the walls of the organ. These hairs are connected to nerves that then transmit the signal to your brain.
Another, similar in principle, way we feel acceleration is via kinesthesia. I.e., the relative position of our limbs, that also changes due to inertia, as long as the accelerating force is applied non-uniformly.
If the force permeats the space in uniform fashion, all parts of your body change their velocities at the same rate, so neither the crystals in your inner ear, nor your limbs ever lag behind, and so, never produce a neural response in your brain.
So, in a way, one could say you never really feel gravity, even sitting in your chair. It's the ground pushing the chair pushing on your bottom parts that disrupts the uniform acceleration of the gravity, providing localised force that then is transferred to the rest of your body through the tissues, with inertial lag across the board.
Now, IF you are close to the source of gravity, the parts of your body farther from the source experience less acceleration(inverse square law) than the closer ones. These are tidal forces that you could feel as being stretched along one axis and compressed along the two other, providing your total length is significant as compared to the distance to the source and its strength(effect also known under the scientific term of
spaghettification).