Wake Island was annexed as empty territory by the United States in 1899 (the claim is currently disputed by the Marshall Islands).

Based on this passage, when was wake island acquired by the us? Let's give stream of consciousness first:
The relevant information to answer the above question is: Wake Island was annexed as empty territory by the United States in 1899 (the claim is currently disputed by the Marshall Islands).
So, the final answer is 1899.