United States-Cuba Relations Normalization Act This bill repeals the trade embargo on Cuba and other provisions restricting trade and travel to Cuba. The bill also (1) removes restrictions on certain transactions related to trademarks used in connection with a confiscated business or asset, (2) extends nondiscriminatory trade treatment to Cuban products, and (3) prohibits and rescinds limits on remittances to Cuba. The President may, in relation to Cuba, impose new export controls and exercise powers related to declared national emergencies. The bill authorizes common carriers to provide telecommunications services between the United States and Cuba. Travel by U.S. citizens and residents to Cuba may not be regulated or prohibited if such travel would be lawful in the United States. The President shall take all necessary steps to engage with Cuba to (1) negotiate settlements relating to claims that Cuba had taken the property of U.S. nationals, and (2) secure the protection of internationally recognized human rights.