The species is not known to use tools in the wild.
Researchers in Austria recorded the cockatoo - named Figaro - repeatedly breaking off splinters from a wooden beam and using them to reach nuts on the other side of his wire enclosure.
The team believe Figaro's feat is the first recorded instance of tool-making among parrots.
The study, published in the journal Current Biology, was carried out at an aviary near Vienna by scientists from the University of Oxford; the University of Vienna and the Max-Planck-Institute for Ornithology in Germany.
"No-one has ever reported [a parrot] sculpturing a tool out of shapeless wood in order to use it later with great sophistication," said Professor Alex Kacelnik of Oxford University, an author of the study.
While birds from the corvid family, such as New Caledonian crows, are known to make tools in the wild, this specialised ability is very rarely reported in other bird species.
Researchers were unexpectedly alerted to Figaro's tool-using ability while he was playing with a pebble and accidentally dropped it out of reach on the other side of his wire mesh enclosure.
After some unsuccessful attempts to reach his toy with his claw, Figaro used a stick from the aviary floor to try to fish for the object, levering it with his beak.
The team then carried out a series of tests that involved placing nuts outside the cockatoo's enclosure, and video-recorded the results.
In the first test, Figaro tried unsuccessfully to reach the nut with a stick that was too short.
He then made his own tool by biting large splinters from a wooden beam. When they were the right size and shape to use as a "raking" tool, he would use them to successfully collect the nuts.
The team repeated the exercise in 10 trials over three days. Figaro was successful each time in making and using tools to retrieve the nut.
The time that it took the cockatoo to manufacture suitable tools also improved over the course of the tests.
"It's almost as if he discovered a solution and then managed to apply it," Prof Kacelnik told BBC Nature.
But he added: "Nobody yet understands in what sense tool-use requires a very high level of intelligence."
While Figaro is alone among Goffin's cockatoos to have been recorded making and using tools, Prof Kacelnik says that his behaviour could display a "level of intelligence for solving a new problem" in the species.