Which act did an appeals court rule Trump cannot use to deport Venezuelan gang members?

The correct answer is the Alien Enemies Act. This piece of legislation, originally enacted in 1798, provides the government with the authority to detain and deport individuals from countries that are at war with the United States. However, the appeals court's ruling indicates that Trump cannot use the provisions of this act to deport Venezuelan gang members because it may not be applicable in a situation where there is not an active state of war declared against Venezuela. The ruling reflects the legal interpretation that the act is intended for scenarios involving wartime threats rather than crime-related concerns involving non-citizens from nations with which the U.S. is not in an active conflict.

In contrast, the other acts mentioned do not specifically pertain to this issue: the Immigration Act primarily addresses immigration policies and laws; the Patriot Act is focused on counter-terrorism measures and domestic security post-9/11; and the War Powers Act relates to the President's power to engage in military action without congressional approval. None of these acts encompass the legal implications related to deporting individuals based solely on gang affiliation from a country without a declared war status, making the Alien Enemies Act the relevant focus in this context.