There were many American policies around the turn of the 20th century that showed that the US had imperial ambitions. America was, at that time, taking direct control of some areas of the world and exercising indirect control over others. Some examples include:
The Spanish-American War. This war was fought in part to show that the US was a major power. As a result of the war, the US took control of Puerto Rico, Guam, and the Philippines. It took indirect control of Cuba as well.
The war in the Philippines. After getting nominal control of the Philippines from Spain, the US fought a bloody war against Filipinos who wanted independence. The Filipinos had thought that the US defeat of Spain would mean independence for them. When they found it did not, they fought the US and the US crushed them and took control of the Philippines.
Annexation of Hawaii. The US tacitly backed the overthrow of the Hawaiian monarchy by American planters. Later, they took control of the islands outright.
The Open Door Policy in China. Here, the US demanded that it be accorded the same powers and rights in China that other imperial countries had.
These are some, but not all, of the policies that show that the US had imperial ambitions at this time in history.