No.
The word sin is used in two different ways:
1. as a non-count noun (the 'sin-disposition' and almost personification):
Christians believe in original sin.
Sin is fundamentally rebellion against God's rules of conduct, an
insistence on one's own way.
2. as a count noun (a particular occurrence, or arguably type):
I gave way to the sin of anger yesterday. (arguably in between non-count and count)
Her sins are many.
The count-noun usage may be encountered in statements such as:
There is not one sin that can be held against you if you are forgiven
on the basis of the substitutionary death of Jesus.
The non-count noun usage may be encountered in statements such as:
Sin will no longer have the hold on you it did before you became a Christian.
Using the preposition on here is really using a staining (or burdening) metaphor, and would require the metaphor to be stated more fully:
She is now washed clean from the stain of sin that was once on her.
The burden of sin on him has now been removed.
And, though contemporary, this type of language is obviously largely confined to the religious domain.