How to write 16bit signet int to SPI SRAM.

Have you searched for the SRAM library for Arduino? I already found it with a search for 23LC512.

Then use e.g. the writeInt() method for writing a 16 bit information to the SRAM, readInt() for reading. You have to provide a new address with each function call. For writing multiple integers you can use writeInts().

For reading readInts() or writing writeInts() multiple integers at once you can use an int array or a struct containing the values, and provide the number of items as the len parameter. See the library and data sheet for more information.