There are many possibilities based on the information you have given:
1. Static electricity charge/discharge. If the air in the room is relatively dry, waving your arm will change the electrostatic charge on your body. The minute static discharge arcs in your clothing may be producing broadband noise picked up by the loop formed from the scope leads to the circuit.
2. Changes in mangetic flux through the scope lead loop to and from the circuit under measurement. Your body is a conductor, and you are moving it through the earths magnetic field in the vicinity of the measurement probe loop. A moving conductor in a magnetic field generates minute curents which, in turn, cause changes in the surrounding field. It's a weak field, and the currents are small, but your amplifier has a large gain.
3. Your body is acting as a reflector for incident RF. There are many sources of RF in our homes - commercial AM and FM radio, TV, shortwave broadcast, computer CPU clocks, microwave ovens, radar, etc. Any non-linearity in the contacts for your scope measurement would act as a rectifier (demodulator). Waving your arm would change the incident RF fields in the region of the scope probe loop. You would see that as a change in the character of the 'noise' displayed on the scope.
Try characterizing the noise - is it broadband, or is it within a narrow range of frequencies? Is it random amplitude, or can you reproduce signals within a defined band of amplitudes? Are you just changing existing noise level, or are you actually creating noise when you wave your arm.
I could go on, but you need to do more measurements to narrow down the possibilities. Shielding your circuit and the scope connections would be a good start. You could then separate out the noise introduced directly into the circuit from the surrroundings, from the noise indroduced through power sources or other connections. Keep in mind that the noise can also be coming from your scope itself.