There could be a few answers to this question. If you were referring to the United States of America, then the first written constitution would be the Articles of Confederation. After the colonists won their independence from Great Britain, they needed to have a plan of government. The colonists wanted to be sure that the new government wouldn’t be able to abuse its powers. This was one of the reasons why they fought for their freedom from Great Britain. They believed the King was abusing his power. Thus, the government created by the Articles of Confederation created a weak federal government. For example, the federal government couldn’t levy taxes or make people join the military. The states held most of the power during the time when the Articles of Confederation was our plan of government.
If you were referring to the first written constitution in the American colonies, it would be the Fundamental Orders that was written in Hartford, Connecticut mainly by Roger Ludlow. Representatives from several different Puritan settlements in Connecticut created a plan of government. This constitution lasted from 1639-1662 when the Charter of Connecticut replaced it.