Is one allowed to hire a non-Jewish rickshaw driver before Shabbos to pick you up on Shabbos and bring you around?

I am not sure what type of rickshaw you are referring to, but the answer would be same, that it is forbidden even in a place that has an Eruv.

Sources:

ראה ציץ אליעזר ח”א סימן כ”א, כו-כז וש”נ.