During a hearing held at Sheffield Magistrates' Court today, Faisal Khan, 23, admitted to one count of sending a text message that is grossly offensive or of an indecent, obscene or menacing character, that was carried out between June 3 and June 25, 2017.
He also pleaded guilty to one count of harassment.
Magistrates released Khan on bail until January 26 this year, when he is due to be sentenced.
As part of his bail conditions, Khan is banned from directly or indirectly contacting Ms Senior, who was awarded an MBE in 2016 for her services for child protection.
Ms Senior collaborated with Times journalist, Andrew Norfolk, to bring the widespread sexual exploitation of children in Rotherham to light following years of inaction by the authorities.