This is a term used among cowboys in the Western and Southwestern United States for a short, thin piece of rope used to tie down young livestock after roping them from horseback by the neck, usually by tying three of four feet together. (In areas of the United States further to the east, Oklahoma, Texas, it is usually called a tie-down string or rope.) The origin in most dictionaries that provide one is "pig + ing" or some variant of that. That seems to me to be a version of a just-so story. No hogs or pigs are customarily roped, and none that I know of are tied down in that way. (Although there is "hog-tied." But I've never seen a hog tied. Maybe I don't run in the right circles.)
Most of the terms used by the working cowboys in the Western and Southwestern United States come from the Spanish or Mexican vaqueros (mounted cowherds, from vaca, cow) who came north with the Spanish and Mexican settlements on land grants in New Spain. For example, the very word vaquero came into use in that area as buckaroo, in the pronunciation of the non-Spanish ranch hands. (There are alternative theories, but that is by far the most probable.) The word still means a man — always a man — who works cattle from a horse, whereas "cowboy" these days means someone who owns a pair of cowboy boots ("shit-kickers"), maybe a wide-brimmed felt or straw hat and a pickup truck. There are many, many other words that came into English from that source: lariat, a rope (la reata); wrangler, a person who tends horses (caballerango->cavarango); remuda, a string of remount horses (remuda), also known as a cavvy, from the same origin as wrangler; hackamore, a bitless bridle (Hispano-Arabic sakimah->Spanish jáquima); chaps, leggings to protect riders against thorny brush, chaparral (chaparreras); and many more.
I think "piggin' string," always pronounced thus by buckaroos, is a word from that set of Spanish/Mexican words that came with the cattle business into what became the US. The land grant haciendas had been there a very long time, already before settlers from the eastern colonies began arriving. Richard Henry Dana, in Two Years Before the Mast, which chronicles his trip (1834-6) from the eastern seaboard around Cape Horn to California, describes in detail his work hauling raw hides down the hills at San Pedro or Point Loma in San Diego and loading them onto the ship Pilgrim. There was plenty of time for those settlers to absorb the practices and terminology of the vaqueros on the ground. The vaqueros used the piggin' string when they were branding calves in the spring. On horseback, they would cut a calf from its mother, haze it over to the bonfire with the hot irons, ride it down and rope it, throw it to the ground, tie up its legs and then brand it. They always carried the piggin' string in their teeth until they dismounted to tie down the calf. You still see this in rodeos and roundups throughout the west still. Here's a roper in Calgary, Alberta, just after leaving the chute to rope a calf:
It seems to me that the vaqueros likely called that small cord, smaller than the catch rope (la reata, lariat) some variation on reata pequeniña (the little rope). In the mouths of the English-speaking settlers, that pequeniña became "piggin," and in conformance with English word order for adjectives and nouns, they tacked the cord part (reata) onto the end as "string": piggin' string.
There's already another model for a similar transformation, where in the Mississippi delta, pequeniño (small child) became "pickaninny." The transformation to piggin' doesn't seem at all far-fetched. Look at the transformation of caballerango to wrangler.
I've been digging into this etymology for a number of years now, but I have found no sources that would confirm it, or even hint at it. I'm a fluent Spanish speaker; the sense of the transformation seems right. "Pig + ing" seems, as I say, to be a just-so story, a folk etymology. But then mine may well be, too.
Does anyone out there have any insight into this, any sources or documents?