The Immigration & Nationality Act requires a U.S. citizen to be 21 twenty-one years of age in order to be eligible to sponsor a parent or sibling for an immigrant visa. For parents, the immigrant visa is immediately available. For siblings, there is a long wait (currently around 11 years).
For all other immigrant visas – including spouses and children – there is no age requirement. However, every sponsor for an immigrant visa must be 18 years old in order to execute a valid affidavit of support. Thus, for all practical purposes, you must be 18 years old to sponsor your spouse or children for an immigrant visa and 21 to sponsor your parents or siblings.