The Twelfth Doctor kept a browser history in his TARDIS's broadband (TV: The Zygon Inversion) and his sonic sunglasses. (TV: Smile)
Handing his sonic sunglasses to Petronella Osgood, the Doctor told her not to look at his browser history. (TV: The Zygon Inversion) Similarly, he told Bill Potts to stay away from his browser history when he left her to the TARDIS's broadband. (TV: Smile)
When the Doctor placed the sonic sunglasses on his first incarnation, his predecessor inquired as to what browser history was. (TV: Twice Upon a Time)