"I want to ask if it is possible for me to connect the output of AND gate to the interrupt directly"

1. Look at the Data sheet for the AND gate - it will give the output specs of the gate;

2. Look at the Data sheet for the AT89s51 - it will give the intput specs of the interrupt pin;

3. from the above results, you can tell whether the gate's output is compatible with the AT89s51's input.


Notes:

You'll still need to debounce it;

You probably don't need an IC AND gate - 4 diodes will probably do!