Legislative Councillor Bernard Finnigan has pleaded not guilty to six charges of aggravated child pornography.
The ruling he has a case to answer is subject to a judicial review.
Mr Finnigan is a former Labor MP and government minister.
He is still drawing a salary of $148,000, but has made little contribution to debate since charges were laid in April last year.
"Given the notoriety of the offences, the nature of the offences and the effect that will have on his capacity to discharge his public functions, that's why I've called on him to resign and that's a matter for him," Mr Weatherill said.