Senators Lidia Thorpe and Mehreen Faruqi will ask the Senate's procedure committee to investigate racism in parliament.

The two senators, who were party colleagues before Senator Thorpe quit the Greens last year, will sponsor a motion to update the chamber's rules to "eliminate language, behaviour, decision-making, and practices that are sexist, racist or otherwise exclusionary and discriminatory".

"Racism in the Senate chamber is routine. Senators dogwhistle and demonise people of colour in speeches, and racist sledging and comments have been made towards Senators of colour, myself included," Senator Thorpe, a Gunnai, Gunditjmara and Djab Wurrung woman, said.

Both senators have been critical of the behaviour in the Senate, with Faruqi - who was born in Pakistan - critical of a censure motion last week against Senator Thorpe for her protest against the King whilst noting no such motion took place in the wake of a tweet by Senator Pauline Hanson where she told Senator Faruqi to "p**s off back to Pakistan".

The tweet was described by a judge earlier month as "an angry ad hominem attack" when finding it unlawful under Section 18C of the Racial Discrimination Act.

"The Senate refused to censure Senator Hanson for racially vilifying me, but they are quick to shut me down for calling out racism," Senator Faruqi said.

"Politicians in here really need a good dose of anti-racism training.

"That's why we are seeking a review of standing orders as recommended by the Jenkins review so we can finally move to eliminate the discrimination, racism and sexism that so many are subjected to and harmed by."

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Last week, Senator Thorpe was censured along with United Australia Party Senator Ralph Babet, who issued a tweet featuring three slurs.

Whilst the motion against Senator Thorpe said the Senate "does not regard it as appropriate for Senator Thorpe to represent the Senate as a member of any delegation during the life of this parliament", Babet's censure motion did not contain such a provision.

Senator Faruqi stated: "Just last week I was silenced in the Senate for calling out racism and white supremacy while speaking in support of Senator Thorpe."

"It seems those running this place have not really listened to what the Set the Standard report had to say about systemic inequality, entitlement and exclusion."

Senator Thorpe said she found it "confronting" to be kicked off a parliamentary delegation to Fiji and Tuvalu because she "dared to call out the king for the genocide of First Peoples", whilst Senator Babet was dealt more leniently by the Senate despite making "appalling racist, homophobic and ableist comments online".

"It shows that if you speak up and demand justice for First Peoples, you will be punished, while racism, homophobia and ableism are not treated seriously by the Senate," she said.

"Discussions of racism might make people uncomfortable, but these are real problems that need to be openly discussed. It's racist in itself to prevent these issues from being raised in the chamber or forcing senators to withdraw."

The two senators said the conditions in the chamber was a "major barrier and turn off" to people of colour wanting to enter politics, arguing racism is "frequently used as a political tool by the major parties".

"They use it to create fear and distrust for their political benefit, and those attitudes flow through to the rest of society," Senator Thorpe said.

"The Prime Minister and opposition leader frequently partake in racist dog whistling.

"This inquiry is about taking a stronger stance on racism and holding this parliament to a higher standard."