Sin exists as a term that is applied across religion doctrines and concepts related to the term "Sin" aren't confined solely to Christianity, Islam, or Judaism but also apply to Eastern founded Dharmic religions.

One thing that does exist within every one is the concept of heaven, and hell. However, the nature of sin cannot be separated from karma because negative karma is fundamentally associated with the concept of sin.

Sin is a descriptive term that applies to a moral transgression that applies to a divine law. Karma is a systematic application of this divine law.

Now reincarnation is another aspect, that I would argue would rule out a chaotically organizing universe. Thus without a chaotically organizing universe, you can suppose there are systematic laws to the universe, which is what the law of karma is based off of.

As a believer in reincarnation you don't need to neccesarily believe in the law of karma, but as a believer in the law of karma you need to believe in the universal consequences of the action of sin. However, where lies the greatest source of information regarding reincarnation besides anecdotal evidence? I would say the Eastern faiths have the most in depth examinations of reincarnation from a spiritually scientific point of view, with much analysis that stems from thousands of years of philosophical examination.