Banton, 23, was recently released by fellow fourth-tier club Wycombe.
"I worked at Crystal Palace with Jason. He brings something different to what we already have which is why I knew he was someone I wanted at this football club," Fullarton told the club website.
"He has trained with us the past two weeks which enabled him to see how welcome he would be here."
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League Two side Notts County have signed midfielder Jason Banton on a deal until the end of the season.