The FDA gives different answers for US citizens and for foreign nationals.
US citizens are generally not allowed to bring "drug and devices" from abroad into the United States (including prescription drugs). However, the FDA has a Personal Importation Policy that may allow it the personal importation of prescription drugs (or OTC drugs or devices, for that matter) under certain circumstances. These exceptions are generally tailored towards situations where a US citizen starts a treatment abroad and needs to bring FDA-regulated products home to complete it, and/or for situations in which an effective drug is not available in the United States.
In most circumstances, it is illegal for individuals to import drugs or devices into the U.S. for personal use because these products purchased from other countries often have not been approved by the FDA for use and sale in the U.S. ... [S]ituations for which this might be allowed: ...
- Product is for the treatment of a serious condition (Prescription Drug Products):
- The product is for a serious condition for which effective treatment may not be available domestically either through commercial or clinical means.
- There is no known commercialization or promotion of the product to persons residing in the U.S.
- The product does not represent an unreasonable risk.
- The consumer affirms in writing that the product is for personal use.
- The quantity is generally not more than a three month supply and either:
- Provide the name and address of the doctor licensed in the U.S. responsible for your treatment with the product, or
- Provide evidence that the product is for the continuation of a treatment begun in a foreign country.
People who are not citizens or permanent residents of the US may bring up to a 90-day supply with them. Larger supplies (for longer visits, say) should be shipped by mail with supporting documentation.
If you are traveling to the U.S. from a foreign country for vacation, attending university, travel for work, etc… The FDA understands that you will need to bring your personal medication while you are in the U.S.
The FDA will allow foreign nationals to bring or ship a 90-day supply of drug products. If the foreign national is staying longer than 90 days, they may have additional medication sent to them.
If you are having medication sent to you by mail or courier, it is suggested that you include documentation that provides evidence that the medication is being sent for your own use while visiting the U.S. This may include:
- A copy of the visa/passport
- Letter from doctor
- Copy of Prescription (in English)
It should be noted that this advice seems to conflate US citizens with US residents, and if strictly followed would present difficulties to (say) a US citizen living in Canada and visiting the United States. I would hope that the FDA would allow US citizens living abroad to follow the "foreign nationals" rules, but bureaucracy being what it is I wouldn't count on it.