Connecting a microcontroller to USB interface
This will require a chip quite different from the MAX232, because RS232 and USB is a completely different protocol. Here, there is some more explanation on that:


  Although RS232 and USB (universal serial bus) are both serial communication standards to connect peripherals to computers, they are totally different in design. A simple cable is not enough to connect RS232 devices to a computer with only USB ports.


Anyway, a chip that you could look at is the USB-DUO series of FTDI: http://www.ftdichip.com/Products/Modules/USBRSxxx.htm (the credits go to John U in the comments). 

Now, there are also microcontrollers that have USB support. That means, they can communicate easily over the USB protocol without an external chip, since they include specific hardware to do this. 

However, a look on the information page 1 shows you that this chip does not have any built-in USB support. If it would have supported USB, there would be some lines like 'USB transceiver', like here.  

Atmel doesn't have any chips in this series (with the 8051 architecture) that supports USB just like they support UART (RS232). To look for a chip that supports USB, you could use the product search.

But note that if you are going to use a chip with a USB peripheral, you cannot just copy the code and have it working for USB. The software needed is completely different. 

Another option, without having to change your current circuit, is using a USB to serial converter. You could use a more common one like here. There are also much smaller types available like this one. You can of course also do it yourself.



1: I'm assuming you meant AT89C51RD2 (a 5, not a 6).