The phrase as it is written here appears in the section, "You Can't Win an Argument," in Dale Carnegie's popular book, How to Win Friends and Influence People.
It is separated from the main text, indicating that it was meant as a quotation and not an original saying, but he gives no indication of where the original saying comes from.
The origin of this old adage appears to go back a long time. So long, in fact, that no one is really sure where it originally came from. It also appears in many different forms in many different places.
Mary Wollstonecraft (1759-1797), the famous British writer and feminist (and mother to the author of Frankenstein), included the quotation "Convince a man against his will, He's of the same opinion still." in the notes to Chapter 5 of her 1792 treatise, A Vindication of the Rights of Woman. This adage is placed in quotes, denoting that it wasn't original text, but without reference to the source. So either she didn't know the origin of this saying or she assumed that it was so popularly known that citing the source was unnecessary.
She might, however, have misquoted two lines from Samuel Butler's (1612-1680) ginormous 17th-century poem Hudibras. Part III, Canto iii, lines 547-550 read thus:
He that complies against his will
Is of his own opinion still
Which he may adhere to, yet disown,
For reasons to himself best known
Butler might have penned an original thought here, or he might have been borrowing what was already an old saying even in his time. We'll probably never know.