Wilson was raised arguably in the most die-hard Calvinist area on the planet; Fife, in the Lowlands of Scotland. His Father was an elder in the Reformed Church, where, it is more than likely, as a boy, Wilson actually watched George Whitefield preach. In all of Scotland, Fife was the heart of Calvinism, the home of St. Andrews University.
There is no record, that I know of, that he affirmed Calvinism, or unitarianism, but, he did believe the scriptures, the least common denominator.
Growing up in the middle 18th century, it doesn't appear the Scottish Enlightenment had a big impact on Wilson, considering he attended Glasgow and Edinburgh Universities a fraction of the time he spent at Calvinist St. Andrews. Wilson was not over-joyed by philosophy:
I prefer the conversation of a fine woman to that of a philosopher.In the Chronicle, Wilson gives his insight as to his opinion on man's reason:
The Visitant, Pennsylvania Chronicle, Feb. 1768. Charles Page Smith, "James Wilson" (Univ. of N.C. Press, Chapel Hill, 1956)
Mathematical knowledge is not received by the senses but rather proved by them. In moral subjects the mind has not such a certain standard; there are numberless passions and prejudices to warp the judgment. It is thus "absolutely impossible," because of the weakness of our minds to have a clear perception of moral truths. "The most important moral truths are discovered not by reasoning, but by that act of the mind which I have called perception...reasoning is very fallacious, for every step leads us into danger, and by one false step we are irrecoverably lost."Hence, Wilson is an important Founding Father, not to be forgotten, or labeled by a tier, whose influences included the "sagacious" "judicious" and "most excellent" Calvinist (sola scriptura, total depravity, salvation by faith alone), Richard Hooker:
The Visitant, Pennsylvania Chronicle, Apr. 25, 1768. Charles Page Smith, "James Wilson" (Univ. of N.C. Press, Chapel Hill)
Hooker's account of natural law appeals to Luther's [and Calvin's] distinction of the twofold use of the law, although his formulation of doctrine is potentially misleading on a terminological level:Thus, to Hooker, and Wilson, the scriptures guide man's reason where enumerated.
The lawe of reason doth somewhat direct men how to honour God as their Creator, but how to glorifie God in such sort as is required, to the end he may be an everlasting Saviour, this we are taught by divine law, which law both ascertayneth the truth and supplyeth unto us the want of that other law. So that in morall actions, divine lawe helpeth exceedingly the law of reason to guide mans life, but in supernaturall it alone guideth. (Lawes I.16.5; 1:139.3-10)
Wilson was one of only six men to sign both the Declaration of Independence and Constitution, the 2nd most active speaker at the Constitutional Convention. Not much is known about his personal faith, or that he affirmed any creed. What we do know is Wilson believed the Scriptures.