Concerned passers-by contacted the Scottish SPCA to say they had spotted a reptile in a stream at Carnwath Golf Course, near Biggar in South Lanarkshire, last month.
Officers initially thought it was a prank but found it was actually a four-and-a-half foot long dead crocodile, which someone had apparently tried to stuff.
The creature was later identified as a West African dwarf crocodile.
The charity says it does not know how old the protected animal was or how it died.
Scottish SPCA inspector Heather Lawson, who collected it, said: "I first thought it was a prank when I received a call saying there had been sightings of a crocodile but when I investigated I found it was real.
"The crocodile was dead and oddly had tape wrapped around its head.
"It seems someone has attempted to stuff the crocodile as it had no insides and there was straw stuck in its legs.
"We found it on May 19 and we've been waiting for identification.
"We now know it was a West African dwarf crocodile and it's a complete mystery how it got there.
"However, we don't know how old it was or how it came to die."
Anyone with information about the crocodile is being urged to contact the SSPCA animal helpline on 03000 999 999.
Ms Lawson added: "These are protected animals and anyone who owns one in this country would need to have a dangerous wild animal licence.
"We are interested in finding out the circumstances and are appealing to anyone with information to contact us."