In Biblical times, women were not necessarily betrothed with rings. For example, when Abraham sent his servant Eliezer to find a wife for Isaac, the betrothal was done with jewelry, but not necessarily a finger-ring. Presumably the custom of betrothing with gifts has been in practice ever since. The first mention of placing the ring on the right forefinger as a wide-spread custom dates back at least about a thousand years as mentioned by Rabbi Elazar of Worms (1165-1238).
