There are accusations that Parliament was bypassed in implementing the contentious plan to manage asylum seekers arriving in the UK.
The chair of the International Agreements Committee, Baroness Dianne Hayter of Kentish Town, said that the deal had not been debated or approved by Parliament before it was signed.
The House of Lords heard this was because the deal was approved as a preliminary agreement, which is not legally binding.
Peers argued that such agreements should not to be used to protect policy from parliamentary scrutiny and debate.
“Perhaps more importantly and certainly more urgently is the issue of deals being signed by way of Memoranda of Understanding rather than by treaty,” Labour’s Ms Hayter told the Lords.
“This means they do not even have to be disclosed to Parliament, let alone laid and debated here.
“I raised this in a private notice question on April 25 in regard to the Rwanda deal – deporting asylum seekers to Rwanda.
“That was done by MoU without any debate or approval by Parliament.
“And I can tell the House that just today, this morning, the committee has launched an inquiry on this and we will have a call for evidence on the MoU on our website shortly.”
The government’s deal with Rwanda has been subject to much criticism, with the UN High Commission for Refugees urging both countries to reconsider the arrangement.
Under the scheme, for which Kigali is set to be paid an initial £120 million ($149.8m), migrants arriving on small boats across the English channel from France will immediately be transferred to Rwanda, where their paperwork will be processed.
Stephen Benn, Labour's Viscount Stansgate and son of the late left-wing politician Tony Benn, said the Rwanda asylum deal was a major political policy development, but the upper chamber “could exercise no scrutiny except to ask a few supplementary questions”.
“That is not good enough,” Mr Benn said.
“I do think that there is a risk that if governments continue to find ways to evade proper parliamentary scrutiny then we are going to get into trouble.
“I hope in future years a future government will make the proper provisions that are necessary.
“If we are going to be a meaningful democracy then this House has to play its full part in it.”
Ms Hayter said that bypassing Parliament with the use of preliminary agreements “flies in the face” of the Ponsonby rule, a 1924 convention whereby significant international agreements are brought before Parliament.
Foreign Office minister Lord Zac Goldsmith of Richmond Park said the non-binding agreement with Rwanda built on wider collaboration with the country, including on climate change and more effective aid delivery.
“A non-legally binding arrangement in the form of an MoU is, the government believes, the most effective vehicle as it allows the partnership to change and the technical details to be adjusted quickly if required, and with the agreement of both partners,” Mr Goldsmith said.
Intervening, Liberal Democrat Lord Jeremy Purvis of Tweed said that Home Secretary Priti Patel and her ministerial colleague in the House of Lords must “correct the record”.
“They have actively misled Parliament by saying these are binding obligations,” Mr Purvis said.
“He has now absolutely contradicted what Priti Patel told the House of Commons and what Baroness Williams told this chamber.
“Both cannot be correct.”
Mr Goldsmith said he was not aware that an error had been made and that a preliminary agreement on international migration was not uncommon.