It has been common as a given name in the English-speaking world only since the 18th century. A famous modern bearer is American actress Julia Roberts (1967-).
The name was introduced to the English-speaking world by E. D. E. N. Southworth's novel Gloria (1891) and George Bernard Shaw's play You Never Can Tell (1898), which both feature characters with a Portuguese background [1]. It was popularized in the early 20th century by American actress Gloria Swanson (1899-1983). Another famous bearer is feminist Gloria Steinem (1934-).
As an English name it has been in use since the Middle Ages, originally in the form Clare, though the Latinate spelling Clara overtook it in the 19th century and became very popular. It declined through most of the 20th century (being eclipsed by the French form Claire in English-speaking countries), though it has since recovered somewhat.