Parents who buy scramblers for underage children could face fines of up to €5,000.
Under a new bill proposed by Fianna Fáil, gardaí could also seize and destroy scramblers and quad bikes used in anti-social manner.
The bill will introduce heavy penalties for parents who buy vehicles for under 18s who go on to use them in a reckless manner.
Between 2014 and 2017, there were 39 deaths related to scrambler incidents, 27 of those were children.
The bill is being brought forward Fianna Fáil Spokesperson on Dublin, John Lahart and the party's Spokesperson on Drugs Strategy and Urban Affairs, John Curran.
"The basic truth is that Gardaí are restricted under current legislation and can neither seize nor effectively police the use of these vehicles," said Mr Curran.
"Under our bill, riding a quad or scrambler bike in an antisocial and dangerous manner will be an offence under Ireland’s public order legislation for the first time.
"In addition, we will deal with the fact that these vehicles are not owner registered by introducing a National Vehicle Register.
"We are looking to include a heavy penalty for those purchasing vehicles for a young person who uses them recklessly.
"Our bill makes provision for increasing the maximum fine to €5,000 and to subsequently allow Gardaí to seize and destroy a vehicle that has been supplied under these conditions."