Key homeland security posts remain unfilled on the anniversary of warning of Russian interference in the 2016 presidential election.
The new requirement could allow immigration officials to peruse the search histories of permanent residents and naturalized citizens.
Secretary Kelly had previously emphasized that the searches, happening at airports and other ports of entry, were targeting foreigners.
The Justice Department told Twitter about the withdrawal of the summons on Friday and that the demand "no longer has any force or effect."
Twitter, which counts Trump among its active users, has a record of litigating in favor of user privacy.
The Secretary of Homeland Security said that European tourists could face tougher vetting at the U.S. border due to the risk of ISIS foreign fighters using the visa waiver system.
Proponents of limiting legal immigration have argued the program gives jobs that Americans could fill to foreign workers at a less expensive cost.