So the apostles and elders in Jerusalem met to decide what Jewish customs these new converts would need to observe. Here is what they came up with:
Acts 15:23-29 (NIV)
This would have been a great time to include instructions on observing other Jewish customs and laws... like tithing.
With them they sent the following letter: The apostles and elders, your brothers, To the Gentile believers in Antioch, Syria and Cilicia: Greetings. We have heard that some went out from us without our authorization and disturbed you, troubling your minds by what they said. So we all agreed to choose some men and send them to you with our dear friends Barnabas and Paul— men who have risked their lives for the name of our Lord Jesus Christ. Therefore we are sending Judas and Silas to confirm by word of mouth what we are writing. It seemed good to the Holy Spirit and to us not to burden you with anything beyond the following requirements: You are to abstain from food sacrificed to idols, from blood, from the meat of strangled animals and from sexual immorality. You will do well to avoid these things. Farewell.
But tithing seems to have been omitted from the requirements of the early church... at least for 500 years or so.