Ms Oswald laid the parliamentary motion in her role as Chairperson of Parliamentary CND.
Mr Kent’s active opposition to nuclear weapons reached its peak during the 1980s, as the UK Government was committing to the Trident submarine programme and American nuclear weapons were sited in the UK.
He served as general secretary and then chair of CND in the 1980s and was an honorary vice-president of CND at the time of his death.
Ms Oswald has been a lifelong opponent of nuclear weapons. Soon after being elected to the UK Parliament in 2015 she was asked to represent the SNP at an event at which Mr Kent was the keynote speaker.
She recalled being overwhelmed at the thought of sharing a platform with such a prominent campaigner but was quickly put at ease by him.
Ms Oswald said: “Bruce Kent was an inspirational figure to people in Scotland and across the UK, and his activism undoubtedly encouraged many people to join the movement against nuclear weapons.
“His legacy will live on as long as people continue to fight against the immorality and waste of resources that nuclear weapons represent as weapons of mass destruction that must never be used.
“Against the backdrop of the horrendous war in Ukraine, it is ever more vital that we work to remove all nuclear weapons from the world’s armouries and Bruce Kent will continue to inspire us in these efforts.”