Wa-alaykum as-salamu wa-rahmatullah wa-barakatuh

In the Name of Allah, the All-Merciful, the Mercy-Giving

All praise is due to Allah. Peace and blessings be upon His Messenger Muhammad.

It is basically permissible to work as a taxi driver. But as in any other job or profession, a Muslim has to abide by the teachings of his religion. Picking a drunk person is not prohibited. If this person carries a bag and you do not know what it contains, then you do not have to inquire. But if you come to know that this person carries wine or the like intoxicants, then you have to refrain from picking him.

Almighty Allah knows best.