RMT union members on the Piccadilly Line - which moves half a million passengers a day and links central London to Heathrow Airport - will strike between 9pm on Wednesday 11 July and 1am on Saturday 14 July.
Trump’s three day visit is due to begin late on Thursday 12 July.
The RMT accused London Underground of failing to employ enough drivers, continued problems with the “ageing” Piccadilly Line fleet and the alleged breaking of agreements.
RMT General Secretary Mick Cash said: “There have been repeated problems on the Piccadilly Line going back a number of years which have led to dispute after dispute and the failure of LU management to get a grip has tipped the situation over the edge yet again. That is why we have had no option but to put on these strike dates.
“Every effort by RMT reps to negotiate a settlement has been obstructed by the company and it is now down to LU bosses to start listening to their members, take the raft of issues at the heart of this dispute seriously and start engaging in a way that will allow us to make some genuine progress.”