The colloquial American-English verb MacGyver means to construct, fix or modify (something) in an improvised or inventive way, typically by making use of whatever items are at hand.

This verb refers to Angus MacGyver, a resourceful secret agent featured as the lead character in the U.S. television series MacGyver (1985-92).

The title role was played by the U.S. actor Richard Dean Anderson (born 1950); this is his photograph, published in The Daily News (Longview, Washington) of Friday 11^th December 1992:

These are the first two occurrences of the verb MacGyver that I have found:

1-: From MacGyvering the Jefferson Way, by Michael J. Demchik, Shepherdstown, West Virginia, published in The Science Teacher (Washington, D.C.: National Science Teachers Association) of January 1992—the author describes the MacGyver Club that he has founded at the high school where he teaches:

The MacGyver television show has been a favorite of mine and my students for the last several years. MacGyver (Michael [sic] Dean Anderson) is a character whose in-depth knowledge of science concepts allows him to get out of one scrape after another. His use of science involves using things that originally had another function. I like to call the process of tinkering and modification “MacGyvering.”
[…]
[…] With the advent of the MacGyver show, I remembered the tinkering and modifying processes and incorporated them into the club.
[…] The students usually had the materials on hand for their designs, but I secretly hoped we would have to spend a little more time “MacGyvering” the materials. There were a few things that had to be “made” specifically for a particular purpose. The students had to take these initial steps and apply them in some new way to a new situation. In this manner, the initial steps of “MacGyvering” have come to pass.
[…]
MacGyvering is a fun, self-initiated, learning experience that can appeal to all sorts of students.

2-: From Partners in Health preparing for airlift to Nicaragua, by Roxane Moore Saucier, published in the Bangor Daily News (Bangor, Maine) of Saturday 23^rd May 1992:

Dr. Robert Bach […], a Bangor surgeon, and his wife, a nurse, have been going to Nicaragua since 1976, providing medical care a couple of times a year in the war-torn coastal town [of Puerto Cabezas]. He does the surgery and she does the organizing, he says.
There are a large number of volunteers involved. Besides Bach there are four other directors of PIH: Gary Moretti, a nurse anesthetist at Eastern Maine Medical Center; Steve Johnson, who has a master’s degree in business administration and has worked in the health-care field; Dr Charles Gluck of Pen-Bay Medical Center; and Dr. Edward Harrow, a pulmonary specialist who has done a lot of work in asthma medicine in Guatemala.
[…]
Johnson will be one of the six or eight volunteers who will spend one to two weeks in Nicaragua this time as will Bach, plumbing and heating specialist Dave Tourtillotte and the bioengineers. The latter will make sure the equipment runs once it gets down there.
“The group has come to realize,” said Harrow, “that bioengineers and plumbers are every bit as important as doctors. You can take a $10,000 piece of equipment, but if you can’t get a 5-cent part, it’s just a piece of junk.”
“They’re really ‘MacGyvering’ things,” Johnson added, referring to the TV show whose hero was always getting out of jams by using makeshift gadgets. That’s especially important because each side of the town has electricity available only every other day—hence the need for generators.

The verb MacGyver has come to be also used figuratively, as in the following from I was my husband’s caregiver as he was dying of cancer—it was the best time of my life, by Tracy Grant, published in the Chicago Tribune (Chicago, Illinois) of Tuesday 6^th September 2016:

During Bill’s last weekend, we had dinner together. At that point, we no longer held onto the illusion of MacGyvering our way out of this predicament, although we still believed that he might come home one more time. We sat side by side on his hospital bed, sharing a Subway sandwich and watching television.