Spacecraft has or have been seen hovering over the White House over the last few weeks.

Spacecraft have been seen hovering over the White House over the last few weeks.

Explanation:

Has is used with singular noun.

Have is used with plural noun.

The term "have" and "has" are used with the pronouns-plural noun and singular noun respectively.

Has is used in the sentence with present tense and present perfect tense.

Have is used in the present tense when the subject is a plural noun or the pronouns.

In the given sentence, spacecraft have been seen hovering over the White House over the last few weeks.