A viscount who threatened Brexit campaigner Gina Miller on Facebook also posted about torturing Tony Blair, a court heard.
Rhodri Philipps, 50, the 4th Viscount St Davids, wrote the message just four days after Ms Miller won a landmark High Court challenge against the Government last year.
He posted: "£5,000 for the first person to 'accidentally' run over this bloody troublesome first generation immigrant."
He described her as a "boat jumper" and added: "If this is what we should expect from immigrants, send them back to their stinking jungles."
Four days later he posted about "torturing Tony Blair, Hilary Clinton, ISIS, Dave (PM) the forgettable, Murdoch..... Oh and that hideous jumped up immigrant Gina Miller".
Philipps, of Knightsbridge, central London, is on trial at Westminster Magistrates' Court for three counts of sending menacing messages on a public electronic communications network.
In another post, in response to a news article about an immigrant, he wrote: "Please will someone 'smoke' this ghastly insult to our country. Why should I pay tax to feed these monkeys.
"A return to Planet of the apes is not acceptable."
In a previous post he said: "I would vote for Trump if I could."
He talked about a "new crusade" and "collective register of Muslims" and added: "Makes the job a lot easier for our collective SIS to track down non-conformists, and frankly, shoot them on the spot".
"The tyranny of Islam and it's ignorant (goat f******) brethren has to be destroyed," he added.
The post was read to court but deemed inadmissible as bad character evidence by senior district judge Emma Arbuthnot.
Ms Miller, 52, said she found his comments about her "genuinely shocking" and felt "violated".
She said she was "very scared for the safety of herself and her family" in a statement read to the court on Monday.
"In addition to finding it offensive, racist and hateful, she was extremely concerned that someone would threaten to have her run over for a bounty," prosecutor Philip Stott said in opening.
"She took the threat seriously, and it contributed to her employing professional security for her protection."
Ms Miller was subjected to a torrent of abuse and threats after spearheading the legal challenge which forced Theresa May to consult Parliament before beginning the formal process of leaving the EU.
The Guyana-born mother of three was seen arriving at court as a witness but did not give evidence as her statement was agreed.
Philipps, also known as Lord St Davids, has accepted writing the posts but said they were not publicly visible and were not menacing.
He insisted he is not racist and told the court: "I know a number of Muslims who are dear friends."
He added: "My own mother is an immigrant from the very same continent (as Ms Miller)."
Philipps, who represented himself in court, admitted during his evidence that he was "incandescent" after Ms Miller's legal challenge.
"She's left a third-world country to come to Britain. It's not for first generation immigrants to behave the way Gina Miller did," he added.
He insisted his posts were meant as "an opening for debate" and continued: "It's how I express myself, not for everyone's taste or liking.
"If you're in the public eye, people are going to say nasty things about you. It's the rough and tumble of public life."
The case has been adjourned until 2pm on Tuesday when a verdict is expected to be reached on the charges.