Rhodri Philipps, the 4th Viscount St Davids, was jailed on July 13 for writing a number of racially and abusive posts on Facebook.
One post read: "£5,000 for the first person to 'accidentally' run over this bloody troublesome first generation immigrant."
Philipps, of Knightsbridge, central London, also called her a "f***ing boat jumper" four days after Ms Miller, 52, won a landmark High Court challenge against the Government.
The 50-year-old, also known as Lord St Davids, accepted writing the posts but said they were not publicly visible and were not menacing.
On Friday he dropped his appeal against his sentence on two counts of sending by public communication network a menacing message after being warned his sentence could be increased if he was unsuccessful.
Philipps served only five days of his sentence before being released on bail while his appeal was pending.
Judge Deborah Taylor, the Recorder of Westminster sitting at Southwark Crown Court, said: "In those circumstances the sentence which was imposed at magistrates courts in full will [re] commence from today."
