You can accept almost anything mutually agreeable to you and the other party as payment. That's the definition of "barter". If you agree to trade manufactured goods for livestock, as long as both parties agree on the terms, I'm not aware of any law that would prohibit it.
I hedged with "almost" because of course you can't accept something that is explicitly illegal. Like you can't say you'll accept cocaine as payment. Less obviously, there are laws regulating the sale of guns, nuclear fuel, agricultural products, etc.
You'd still have to pay taxes, and it can get complicated to determine the taxable value of the transaction. Sorry, but you can't avoid taxes by getting your income in something other than cash.
Sigh. In response to Mr Rayburn, let me be more explicit about "I don't know of any law". I search the US Code for the word "barter". Using this web site I found 88 hits. https://uscode.house.gov/search.xhtml?searchString=barter&pageNumber=1&itemsPerPage=100&sortField=CODE_ORDER&action=search&q=YmFydGVy%7C%3A%3A%3A%3A%3A%3A%3A%3Afalse%3A%7C%3A%3A%3A%3A%3A%3A%3A%3Afalse%3A%7Cfalse%7C%5B%3A%3A%3A%3A%3A%3A%3A%3Afalse%3A%5D%7C%5B%3A%5D The only cases in which they say that barter is illegal are cases where ANY sort of transaction is illegal, and they include barter to be complete. For example, there's a law against the unlicensed selling of bald eagles, 16 USC 668, that begins, "Whoever, within the United States or any place subject to the jurisdiction thereof, without being permitted to do so as provided in this subchapter, shall knowingly, or with wanton disregard for the consequences of his act take, possess, sell, purchase, barter, offer to sell, purchase or barter, transport, export or import, at any time or in any manner any bald eagle commonly known as the American eagle or any golden eagle, alive or dead, or any part, nest, or egg thereof of the foregoing eagles, or whoever violates any permit or regulation issued pursuant to this subchapter, shall be fined not more than $5,000 or imprisoned not more than one year or both." Note that the relevant point here is that you can't possess, sell, OR barter. You can't engage in any sort of trade or transaction in bald eagles.
Similarly there are other laws that prohibit sale, barter, etc of illegal drugs, government property, etc. But in all the laws that I could find, no distinction is made for barter. It's not that you can sell but not barter. Barter is included in the list of illegal transactions along with selling, etc.
BTW it occurs to me that a law against barter but permitting selling would be very difficult to enforce. What if the people involved just said, "Oh no, you misunderstand. I didn't trade my bicycle for a microwave oven. I sold him my bicycle for $100 and he sold me his microwave oven for $100. We did the two transactions at the same time so there was no need to hand the cash back and forth."
