I am planning to travel to the US and buy a prepaid internet SIM card so I am able to use Uber. Since I will be replacing my current SIM card with that one that only provides internet service I won't be able to make/receive calls or text messages. Will that be a problem for using Uber?
It should be usable, but there's a potential for a few complications:
Uber generally requires that you confirm your phone number with a text message when you register for an account. You should make sure you do this at home before you travel. If you don't already have an account, make sure you get a friend's referral code and you'll each get some free credit.
Text messages and calls are generally part of the Uber service. You'll be sent a text message when the driver is close to alert you to come outside and be ready. This message is fairly superfluous though; you can see the same information by keeping the app open and being ready to meet your driver as the car approaches.
The bigger issue are the calls. Sometimes, the driver may call you (or you may want to call the driver), such as if they want to confirm the pickup location or they aren't sure where you are. This could lead to confusion or perhaps cancelled rides. To avoid help this, be careful to ensure the pickup location is set exactly where you plan to be (don't just rely on the GPS to drop the pin, as it's not always perfectly accurate) and allow a little extra time in case you need to request another ride.