The RS-232 signal is the very same regardless of Vcc.
Can I connect direct the UART serial port of AT89S8252 to the phone
No, you need an interface chip. Direct from the UART pins is something that is the VERY EXCEPTION to UART use.
but on the other hand all data cable with the MAX232 or compatible for this phone uses 5V power supply too.
I guess that the chip in the cable convert RS-232 from the outside world to logic levels for the phone. If that is the case, you need a MAX232 type chip between your uC and the cable.

Happy new year

Erik