The 213th mitzvah is that we are commanded to acquire [by kiddushin1] a woman before2 marrying her [n'suin]: either by giving her something3 [of sufficient value]; by giving her a document [of marriage]; or by having marital relations [for the purpose of kiddushin]. This is the mitzvah of kiddushin.
This mitzvah is hinted to in the Torah in the verse,4 "When a man acquires a woman and has relations with her...." This implies that he can acquire her through having relations.
[That a document may be used is alluded to in the verse5 which states that after receiving a writ of divorce,] "She leaves...and may marry another man." [Since the divorce and the marriage are described together, they can be compared:] just as she leaves by means of a document, so too she may marry by means of a document.
So too, the use of money may be derived from the verse6 regarding a Jewish maidservant,7 [that upon reaching puberty, she goes free,] "without money." Our Sages explain,8 "There is no money received by this master, but another master does receive money. Who is this? The girl's father [who receives money when his daughter gets married]."9
However, only kiddushin by means of relations has the validity of a law m'dioraysa,10 as explained in many places in Kesuvos,11 Kiddushin,12 and Niddah.13 All the details of this law have been thoroughly explained in the designated tractate, i.e., Kiddushin.
Our Sages stated explicitly14 that kiddushin by means of relations is a Torah law. This statement proves that kiddushin counts as a law of the Torah.
