Where did the concept of the chosson (groom) giving the kallah (bride) a ring, specifically, for kiddushin (i.e. under the chuppah) come from?
The Minhag is mentioned in sources as early as the Teshuvas HaGeonim (Harkavy no. 65) and the Zohar, quoted by the Rama in Even Ha'Ezer 27:1. It is indeed a Minhag, and is quoted as such in many places (such as here, the Nitei Gavriel)
The Rogotchover in his commentary to Rambam Ishus 3:1 gives the custom a creative halakhic basis: today, when Kiddushin and Nisuin are practically simultaneous, it's crucial that the man give the woman something that would actually belong to her even after the marriage is completed (at which point the husband gains most of her property). Therefore, the man should give the woman a piece of jewelry since he doesn't have rights to her clothing or jewelry (and rings are pretty much the only piece of clothing that can be carried around conveniently). This is somewhat questionable, however, as the object (whatever it may be) would belong fully to the woman for the brief interim period, the Rogotchover brings support for his position from a Ran (ד"ה מנה אין כאן) that such an object might not be able to be considered to have completely left the ownership of the man.
This post from a blog of divrei Torah by Rabbi Eliezer Eisenberg provides several other reasons:
- There is one passuk in which the letter Mem in middle of a word is formed like a mem sofis, an end-of-word Mem, the passuk in Isaiah 9:7-לםרבה המשרה ולשלום אין קץ. The Tikunei Zohar mentioned in the Rama in 27 says this letter Mem is ring shaped, and it alludes to the peace and fertility we portend for this couple. The Gematria of לםרבה is Eizer and Zera. This Zohar is also brought more clearly in the Levush here in siman 10.
- The Sefer Chinuch Mitzvah 552, it is a reminder to her and to all that she is a married woman. (Eliezer Eisenberg: One assumes that she doesn't need the reminder on Shabbos, since the halacha used to be that it was assur to wear jewelry on Shabbos. Unless this doesn't have a din of jewelry, which I doubt.)
- In Parshas Mikeitz we see that Pharaoh gave Yosef his ring as a sign of trust and high office and responsibility. We find the same with Achashveirosh and Haman. So, too, when a woman becomes the Akeres HaBayis, she receives the ring of honor, responsibility, and trust. אוצר כל מנהגי ישרון
- A ring joins two objects, as do the taba'os of the Krashim of the Mishkan and of the Choshen and Eifod. This ring joins the husband and wife. לקוטי מהרי"ח
- A chain is made up of rings. The creation of a new family forges another link in the chain of mesora of Klal Yisrael, the Shalsheles HaYuchsin. ספר המטעמים אות לא
- Through marriage, the Shechina is shoreh in a house. The ring is a symbol of the Shechina because it has no beginning and no end.
- I'm not sure this counts as a reason, but the Mordechai in Kiddushin 488 says that a 14 K gold ring is something that doesn't need evaluation, it has inherent value according to its weight. (In fact, some communities use silver rings; it is possible that this is based on the din of כספא טיבעא.) Perhaps that's why a gold ring is used, because clothing or gems or things need assessment. Even coins used to vary according to whether they were used locally as currency. The value of a simple piece of gold is pretty universal, the same all around the world, except, of course, in places of unusual circumstances like war or famine. The Mordechai- העם נהגו לקדש בטבעת של זהב בלא אבן יקרה בתורה משום דרוב בני אדם אינם בקיאים בשומא
The Nittei Gavriel also brings this minhag of using a silver ring (instead of the more common practice to use a gold one), though I don't think that I've ever seen that done myself.