No, Muslims are strictly prohibited from marrying their own sister.
Islamic Law on Marriage to Siblings
The Quran explicitly forbids marriage between siblings. Chapter 4, verse 24, outlines those who are forbidden in marriage, which includes one's sisters. This prohibition is absolute and universally accepted within all schools of Islamic thought.
Quranic Basis
The prohibition is rooted in the Quran, which clearly identifies close blood relatives, including sisters, as being forbidden in marriage. This divine decree leaves no room for interpretation.
Kinship Terminology Clarification
It's important to distinguish between a sister and other female relatives, such as cousins. Islamic law permits marriage to cousins (father’s brother's daughter, father’s sister's daughter, mother’s brother's daughter, and mother’s sister's daughter), although cultural preferences may vary. However, there is absolutely no allowance for marriage to one's biological sister.
Summary
In summary, marriage between a Muslim and their biological sister is unequivocally forbidden in Islam, based on clear prohibitions within the Quran.