Leona O'Neill, 29, Poppy Kohner, 30, Hannah Downie, 25 and Louise Dear, 30 allegedly "behaved in a threatening or abusive manner likely to cause a reasonable person to suffer fear or alarm" by climbing the crane.
Kohner from Glasgow's West End, and the others - all from Govanhill, also face a charge of wilfully or recklessly destroying property belonging to another.
The are accused of using bolt cutters to cut a heavy duty hasp to gain access to crane and damaging the hasp.
All four women appeared from custody yesterday at Glasgow's Justice of the Peace Court where they were each represented by Ross Yuill.
They denied the charges and a trial was set for December, and they were released on bail with the condition not to go within 50m of the crane.