The term was adopted by computer scientists when they applied mathematical reasoning to programming in the mid 20th century.
The word argument has the general sense of something from which another thing may be deduced. It comes ‘from the L. arguere “make clear, make known, prove, declare, demonstrate,” from PIE argu-yo-, from root arg- “to shine, be white, bright, clear” ’, which root is also preserved in the words argent (“silvery white”) and Argentina (“[river] of silver”).¹
Its use in English to mean a “mathematical quantity from which another … quantity may be deduced, or on which its calculation depends” is attested as early as 1386:
deduce: 추론하다
Argument (ā·ɹgiuměnt). [a. F. argument (13th c.), ad. L. argūment-um, f. arguěre (or refashioning, after this, of OF. arguement, f. arguer): see ARGUE. For use of the L. form, see 3 c.]
2. Astr. and Math. The angle, arc, or other mathematical quantity, from which another required quantity may deduced, or on which its calculation depends.
c 1386 CHAUCER Frankl. T. 549 Hise othere geeris, As been his centris and hise Argumentz.
c 1391 — Astrol. xliv. 54 To knowe the mene mote and the argumentis of any planete.
1796 HUTTON Math. Dict. I. 141/2 Annual argument of the moon’s apogee . . is the distance of the sun’s place from the place of the moon’s apogee.
1879 THOMPSON & TAIT Nat. Phil. I. 1. § 54 An arc of the circle referred to . . is the Argument of the harmonic motion.²
According to Wiktionary, the originating Latin word was argumentum, which also means "token". So you can see pretty easily how that term got used in mathematics, most of the texts of which were written in Latin for a long time.
A lot of terms used in mathematics, particularly around functions, naturally spread to programming.
The word argumentum does not mean “token”, not in the sense used in mathematics and computer science (a symbol). In this context, token means “evidence” (literally “a showing”), as you might see it in phrases such as “a small token of my esteem” or “gave the proposal only token support”.