No. Gifts are not taxed to the recipient, regardless of amount or whether they are from people in or outside the United States. If you make gifts, you need to check on whether you must pay any gift tax (not income tax) and/or whether you have to file a gift tax return, Form 709.
An arrangement under which one person transfers legal ownership of assets to another person or corporation (the trustee) for the benefit of one or more third persons (beneficiaries).