Hans Christian Ørsted determined in 1820 that the electrical charge in a wire deflected an external magnetic field. This is because when you pass an electrical current through the wire it emits it's own magnetic field. This matters because if you coil that wire the field of the adjacent windings overlap with each other. This cancels out electromagnetic noise from sources outside of the wire. Thus was born the twisted pair US patent # 220791. Thank you Alexander Graham Bell. More here. We still use twisted pair cable in Ethernet cable today. It's been over a century and the design remains in use. But Bell didn't invent twisted pair cabling until 1881, That's 60 years later. There was no direct link between Oersted and Bell. It was 1880. They never met and he couldn't just Google it.
Hans Christian Ørsted was Danish, and big on chemistry, physical and post-Kantian. He was also one of the earliest thinkers to describe the "thought experiment." He also discovered Aluminum. He was a clever bloke in other words. The oersted (Oe), a unit of magnetic H-field strength, is named after him. It's a nice way to be remembered. In 1820 during a lecture, Ørsted noticed a compass needle was effected by the toggling on and off of the current form a battery. It proved a connection between electricity and magnetism. That is as far as he got.
Literally a week later André-Marie Ampère began a series of papers describing mathematically how this worked. He also later demonstrated that two parallel wires could be attracted or repulsed by one another, depending on what direction current flowed through them. More here. Shortly thereafter Johann Schweigger deduced that multiple turns of wire amplified the effect the electromagnetic effects of electrified wire on a compass needle. We now call that a Schweigger's coil. Schweigger was a professor of chemistry at the University of Halle in Germany. Ampère used simple galvanometers like this to measure his experiments.at the time they were called multipliers. Another German, Johann Poggendorf built a multiplier in 1821. University of Cambridge professor James Cumming built a galvanometer with the addition of a magnet to offset the magnetic pull of the Earth. These designs inspired scientists like Prof. Joseph Henry and William Sturgeon to build electromagnets. More here. By 1828 Henry had made magnets that could lift hundreds of pounds. With twisted wires he made simple electric motors. One such diagram describes the wiring
"The galvanic magnet A B is wound with three strands of copper bell wire, each about twenty-five feet long; the similar ends of these are twisted together so as to form two stiff wires q r, which project beyond the extremity B, and dip into the thimbles s t."Another pre-Bell telephone inventor (there are a few) named Antonio Meucci may have also invented twisted pair. In one of his patent drawings from 1858 he indicated two pairs of two wires each. It is unclear if they were twisted, but it's also not clear why he would have configured a 4-wire circuit for any other reason. It's equally notable that patents by Elisha Gray do not indicate multiple wires on each path. So he is another early contender.
Now you don't actually have to twist the wires together to get some of these noise-rejecting EM effects. Just winding them helped, and even just having them close together did as well. It is highly probably that some engineers running telegraph lines were aware of the noise reduction. But they didn't patent it, or didn't think of it as patentable. So look at that image at the top of the post. The outer coil is coiled, and the inner wire a set of three twisted wires. That's an image of a marine telegraph line, the original Atlantic cable, run by Mr. Cyrus Field, completed in 1858. It was a Kerite cable. More here. It predates Bell by 20 years but it's still not a twisted pair. Close but no cigar.