Measuring low currents with oscilloscope - does the current really flow backwards this much?
For the sake of discussion, let's assume that the MCU absorbs around 1mA (I suspect much less, actually). This means 2mV across the sensing resistor, which is pretty low. I think you are just measuring common mode noise, and your DC component is swamped by that.

You could try to activate an averaging acquisition mode, averaging over several waveforms. You should see some improvement. 

You could also try to deactivate all possible sources of interference in the room (if you have LED lighting fixtures their power supply could contribute to the radiated and conducted noise, for example).

Try also to avoid using the ground clip of your scope probe: that acts as an antenna! Locate a ground point near your resistor and connect to it using this kind of probe accessory:



EEVBlog #441 - "How to track down common mode noise" gives additional hints and I think it's relevant.

Anyway to measure such tiny currents you may need some additional amplification. Dave Jones, from EEVBlog, has designed his &mu;Current amplifier just for this kind of things.