Yes. US citizens must have a visa to travel to Iran. You will not be allowed to enter the country if you arrive without a valid visa, and some US citizens holding valid visas have still been denied entrance for no apparent reason.
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Safety for Solo Female Travelers in IranIran is a safe destination for solo travelers, although it's important to be aware of the local customs and laws, especially for women. Solo female travelers may experience some discrimination, and it is important to dress modestly and cover the head and hair with a scarf.
Iran's tourist visa is issued for up to 30 days and can have up to two additional 30-day extensions, for a total of 90 days. To get a visa prior to arrival, a Visa Authorization Code must be applied for through the Iranian Ministry of Foreign Affair's e-visa website or an Iranian travel agency.