The definite article, the sin, shows that Jesus does not mean merely a simple act, but a life of sin. Compare 1Jo 3:4-8, and doeth the truth (Joh 3:21); doeth the righteousness (1Jo 2:29).
The servant (δοῦλος)
Or, a servant. Properly, a bond-servant or slave. See on Mat 20:26.
Of sin
A few authorities omit, and read whosoever committeth sin is a bond-servant. Compare Rom 6:17, Rom 6:20.