Answer:
No, he never received his commission and became a justice of the peace in the district of Columbia.
Step-by-step explanation:
William Marbury was appointed Justice of the Peace for the District of Columbia in the latest days of John Adams's presidency. Along with Marbury several dozens of Justices were appointed by Adams in an attempt to frustrate the next elected president Thomas Jefferson.
Marbury never received the commission because it was blocked by the new Secretary of State James Madison. Knowing that he was appointed and he had never received the commission Marbury went to the U.S. Supreme Court asking them to issue a writ of mandamus forcing Madison to deliver the commissions. The Supreme Court noticed that Madison´s attitudes were wrong but also noticed that the law by which Marbury went to the Supreme Court was against the United States Constitution. Justice Marshall stated that Congress had expanded the powers of the Court more than what the U.S. Constitution had planned.
Marbury never held a judicial office.
I hope this answer helps you.