Is there any way I can connect the RAM of a computer to Arduino?
No, you can't connect your normal desktop computer memory to your Arduino. For a number of reasons:


Computer memory (at least for the past 20 years) is DDR SDRAM. That's Synchronous Dynamic RAM. It requires very strict timing and synchronous (clock based) data transfers with clocks measured in the hundreds of MHz - something the Arduino cannot do.
You need lots and lots of I/O pins to interface with SDRAM. I mean, just look at all those pins - how would you connect all those up to a little Arduino?
Being DRAM you need to use quite a complex process to keep the data refreshed and stop the capacitance of each cell from draining away. Yes, that side of things is do-able, but not child's play.


The only way you will be able to interface DDR SDRAM with an Arduino is through some intermediate interfacing system that can do all the above for you. Your best candidate is to design an SPI to DDR conversion chip using an FPGA and Verilog or VHDL. That way you can communicate with the FPGA using SPI (or you could choose I2C if you like, or a simple 8-bit parallel protocol) and the FPGA then does all the grunt work that the Arduino isn't capable of.

However, while you're at it, you may as well put a CPU core in the FPGA (e.g., NIOS II or something) and do away with the Arduino altogether...