Fashion and restaurant mogul Richard Caring is offering the cash reward following the shooting on 13 September at his 500-acre estate, Pixton Stables.
Estate manager Alex Cheyne said the carcase was of a six-year-old stag, one of 20 red deer in an enclosed area in front of the property.
?The stag had two bullet holes in the neck that look as though they are from a low calibre rifle, possibly a .22,? added Mr Cheyne.
?What has made us so angry is that it looks as though it has been done simply for pleasure.?
To contact Mr Cheyne with information about the incident, call 01398 324243.