tl/dr; No, a slave could not own a patent because the laws of the United States did not recognize slaves as citizens. Since obtaining a patent required that applicants swear an oath of citizenship, enslaved persons could not apply for patents.
Accodring to H.E. Baker ("one of the most useful men in Washington", the Second Assistant Examiner at the Patent Office in the 1880s, valedictorian of his law class and postgraduate course, and a black man) in "The Negro as an Inventor":
In law, a patent is a contract between the government and the inventor or his assignees. The slave, although the inventor, could not under the law be a party to a contract, and therefore could not secure the patent himself.
Baker further states that the government had a theory that "a slave could not take out a patent for his invention". (p400).
Generally, slave owners could not patent inventions of their slaves. There were some exceptions made in the Confederacy's patent laws.
Below is a copy/paste of selections from "Invention of a Slave" by Frye:
The antebellum Patent Act was amended and rewritten several times. After 1793, it included a “Patent Oath,” which eventually required patent applicants to swear to be the “original” inventor of the claimed invention and to their country of citizenship.This oath effectively precluded slave owners from patenting the inventions of their slaves. Additionally, it limited patents to “citizens of the United States.
On June 10, 1858, the Attorney General issued an opinion titled Invention of a Slave, concluding that a slave owner could not patent a machine invented by his slave, because neither the slave owner nor his slave could take the required patent oath. The slave owner could not swear to be the inventor, and the slave could not take an oath at all. The Patent Office denied at least two patent applications filed by slave owners, one of which was filed by Senator Jefferson Davis of Mississippi, who later became the President of the Confederate States of America. But it also denied at least one patent application filed by a free African-American inventor, because African-Americans could not be citizens of the United States under Dred Scott.
Slave owners unsuccessfully tried to amend the Patent Act to enable slave owners to patent the inventions of their slaves, which the Patent Act of the Confederate States of America explicitly permitted. By contrast, abolitionists successfully convinced the Attorney General [in 1862] to issue an opinion concluding that free African-Americans were citizens of the United States, entitled to patent their inventions, among other things.
However, before Dred Scott, free African Americans could receive patents.
The first known [free] African-American inventor to receive a patent was Thomas Jennings, who patented a method of “dry scouring” clothing in 1821.
But there were also many enslaved antebellum African-American inventors who could not patent their inventions, or own property of any kind. Some slave owners probably surreptitiously patented the inventions of their slaves. At least apocryphally, Eli Whitney’s cotton gin was actually invented by a slave named Sam. Likewise, Cyrus McCormack’s mechanical reaper is often attributed to a slave named Jo Anderson
Some further reading:
"Race and Selective Legal Memory: Reflections on Invention of a Slave" by Professor Kara W. Swanson, J.D, Ph.D.