Yes. Unlike its requirement that the President be a "natural born" citizen, and the Senators and Representatives be at least "naturalized," the Constitution is silent on the citizenship and residency requirements for a Supreme Court Justice.
Six Supreme Court justices were born outside the United States; however, only two listed* would be considered naturalized citizens under the laws operating at the time.
David Brewer...........1889-1919........(Turkey) (born to American missionaries)
George Sutherland was born in Buckinghamshire, England, in 1862, and emigrated to the United States with his parents in 1863.
Sutherland attended the University of Michigan Law School, but left without earning a degree. He was admitted to the Michigan bar in 1883, then briefly entered private practice with his father, who had also become an attorney.
Prior to joining the Supreme Court, Sutherland was a member of the House of Representatives (1901-1903) and US Senator from Utah (1905-1917).
Warren Harding nominated Sutherland to the Supreme Court in September 1922. He was part of the ultra-conservative bloc of the Court, known collectively as the Four Horsemen, who opposed Franklin D. Roosevelt's New Deal legislation. Sutherland retired from the Court in 1938.
Felix Frankfurter (1882-1965), who was born in Austria and immigrated to America with his parents at the age of 12, graduated from Harvard Law School, and went on to become assistant to Henry Stimson (later Secretary of State under Hoover) as US Attorney for the Southern District of New York. He later followed Stimson to Washington when President Theodore Roosevelt appointed Stimson Secretary of War.
Frankfurter was was a staunch supporter of Roosevelt, and worked on the "Bull Moose Campaign" of 1912, in an unsuccessful attempt to return Teddy to the Presidency after he lost the Republican nomination to William Howard Taft.
After World War I, Frankfurter returned to Harvard as a Law Professor, where he remained until Franklin D. Roosevelt was elected in 1932. Frankfurter, an ardent supporter of President Roosevelt's New Deal, became a close and trusted advisor to the President. This lead to his nomination to the Supreme Court in 1939 (where he served until 1962).
Although ideologically liberal, Frankfurter was the Court's most outspoken proponent of "judicial restraint," the belief that the Court should not interpret the law and Constitution in such as way as to place encumbering limits on the power of the Legislative and Executive branches. Although foreign-born, Frankfurter revered the Constitution and was considered extremely patriotic.
Recent Supreme Court Hopefuls
More recently, two-term Michigan Governor Jennifer Granholm, a naturalized citizen and Canadian by birth, was under consideration for nomination to the Supreme Court seat vacated by now-retired Justice David Souter, but her foreign birth (despite Canada being a neighboring country) became a major point of contention with political conservatives.
You can draw several conclusions from this brief history: At present, Supreme Court Justices are most likely to be drawn from a pool of "natural born" citizens, but this is due to political considerations, rather than law. Naturalized citizens are eligible to serve on the Court. In order to become a naturalized citizen, a person must be at least 18 years old and must have been a permanent resident in the United States for at least five years, or for three years, if married to and continuously living with a spouse who's an American citizen. A person voluntarily serving in the US military is eligible to apply for citizenship after one year of service, or within six month of being honorably discharged.
Non-citizen residents of the United States may or may not be legally eligible for a position on the Court, but politically, the likelihood of a non-citizen being nominated or confirmed by the Senate is virtually nil.