The Scottish SPCA said it had been contacted with concerns that the practice is taking place in East Ayrshire, particularly in Auchinleck and Cumnock.
It has asked people to look out for snares or deer that appear to have died under suspicious circumstances.
There are no circumstances in which it is legal to snare a deer and anyone suspected of doing so could be subject to criminal proceedings, the charity said.
Chief superintendent Mike Flynn said: "Deer are very powerful animals and when made captive they panic in a bid to escape, often pulling so hard they cause serious injury to themselves, which is often fatal.
"The sheer suffering involved is extremely concerning and deer snaring is an area of priority for our special investigations unit.
"While snaring continues, suffering will continue, and that is why we are in favour of an outright ban."