How do I force Adobe Camera Raw to use monitor color profile ?
You probably can't without some serious hacking, but device profiles should not be used for editing anyways. If you insist on converting the image to device profile, use ProPhoto RGB and do Convert to Profile (specifying the device profile) later in PS.
I shoot in RAW. sRGB is set on camera.
The sRGB setting in camera does not have impact here. It is used for the embedded jpg preview and for the actual image only if you shoot jpeg.
The problem is that after I open my photo in Photoshop and enable
"Proof Colors" (set to "Monitor RGB") it looks pretty different that
it was in Adobe Camera Raw (ACR).
I think this is a sign that there is something wrong with the soft proof setting or the Monitor RGB profile is not actual measured profile of the monitor in its current setting.
That means I can't do color correction in ACR.
The colors you get and see in ACR are probably more correct than those you see in the soft proof with Monitor RGB. I only use soft proof for print preparation, but if I wanted to figure out what is wrong with the Monitor RGB profile, at this point I would recalibrate my display, get one or more of the test images available on the internet to verify the soft proof is working correctly, shoot Xrite Color Checker and see if the representation in ACR or soft proof is correct. I would also try soft proof with sRGB, which should not change the colors compared to ACR almost at all.