Potentiometer Deadzone noise?
At some point as you rotate the pot through 360 degrees, the connection must be  broken (or must momentarily short) as the wiper goes from one end to the other of the element. 

When the wiper connection is broken, you have a 1M resistor to ground. 1M is not a low enough impedance to reliably read 0V on an MCU ADC. 

If you really want this to work you will have to use a rail-to-rail input and output op-amp as a buffer, and it must have input bias current that is low enough (say &lt; 1nA). 

You could also just lower the 1M to something like 10K (better to move it to the other side of R3) but it would adversely affect the linearity of the signal (correctable in software at some smallish loss in resolution). 

Deviation from linearity is maximum at ~2/3 of rotation. It's a simple quadratic to do the correction as below (409.6 counts is exactly mid-rotation of the pot, assuming a 10-bit ADC). 

reading / corrected reading
0   0.0
16  16.2
32  33.0
48  50.2
64  68.0
80  86.2
96  104.8
112 123.9
128 143.4
144 163.3
160 183.5
176 204.1
192 224.9
208 246.0
224 267.2
240 288.6
256 310.0
272 331.6
288 353.1
304 374.5
320 395.9
336 417.1
352 438.2
368 459.0
384 479.6
400 499.9
416 520.0
432 539.7
448 559.1
464 578.1
480 596.7
496 615.0
512 632.9
528 650.4
544 667.5
560 684.2
576 700.5
592 716.4
608 731.9
624 747.1
640 761.9
656 776.3
672 790.3
688 804.0
704 817.4
720 830.4
736 843.1
752 855.4
768 867.5
784 879.2
800 890.6
816 901.8
832 912.6
848 923.2
864 933.6
880 943.6
896 953.5
912 963.1
928 972.4
944 981.5
960 990.4
976 999.1 
992 1007.6
1008 1015.9
1024 1024.0