Does a taxi driver have to pay zakaah?

Firstly: 

Cars that people own are of two types: 

(i)Cars that are prepared to be bought and sold. Zakaah is due on them because they come under the heading of trade goods

(ii)Cars that are prepared for hire, or for personal use. No zakaah isn due on them, because of the hadeeth narrated by al-Bukhaari (1464) and Muslim (982) from Abu Hurayrah (may Allah be pleased with him), that the Messenger of Allah (blessings and peace of Allah be upon him) said: “The Muslim is not obliged to give zakaah on his slave and his horse.”

Al-Nawawi (may Allah have mercy on him) said: This hadeeth establishes the principle that that no zakaah is due on property that one keeps; there is no zakaah on horses or slaves if they are not intended for trade. End quote from Sharh Muslim by al-Nawawi. 

“Property that one keeps” is that which a person keeps to use and benefit from, not to sell it and trade in it. 

For more information please see the answer to question no. 146615. 

Secondly: 

If a person has a car that is for hire (i.e., a taxi), whether he works in it himself or has someone else working for him, no zakaah is due on the car itself – as stated above; rather zakaah is due on the money that the car driver earns. That is subject to two conditions: 

(i)That the money he earns from hiring out the car reaches the nisaab (minimum threshold)

(ii)That one full hijri year has passed since that amount of money earned came into his possession.

Shaykh Muhammad ibn Ibraaheem (may Allah have mercy on him) was asked: A man has a car by means of which he earns a living by driving it from one city to another. Does he have to pay zakaah on it, or on the income he earns through it? 

He replied: There is no zakaah on it if he does not intend it to come under the heading of trade goods. Zakaah is only due on what he earns from using it, if his earnings reach the minimum threshold (nisaab) and one year has passed since he acquired it. End quote from Fataawa wa Rasaa’il Samaahat al-Shaykh Muhammad ibn Ibraaheem, 4/105. 

Shaykh Muhammad ibn ‘Uthaymeen (may Allah have mercy on him) was asked: Is zakaah due on cars that are hired out or private cars? 

He replied: Cars that are hired out for transportation or private cars that a person uses for his own purposes are not subject to zakaah. Zakaah is only due on the fees earned if they reach the minimum threshold by themselves or when added to other money that he has, and one year has passed since acquiring it. The same applies to property that is prepared for renting out. There is no zakaah on it; rather zakaah is due on the rent paid. End quote from Majmoo‘ Fataawa Ibn ‘Uthaymeen, 18/228. 

To sum up: if your brother has not earned from working in the car enough money to reach the minimum threshold, or the money reaches the threshold but he has spent it on his needs before one year passed since he acquired it, then no zakaah is due on it. 

And Allah knows best.