Arduino I2C via USB Serial cable? An Arduino UNO is given.
I want to establish an I2C communication channel between Arduino UNO and a Linux Machine which have only USB ports available to communicate with peripherals. 
Currently I can communicate with Arduino board via USB Serial cable (TXD and RXD which are on pins D0 and D1).

My question is: is there any way to use those pins as SCL/SDA to communicate via I2C with Arduino Board?

I am thinking that the only way to accomplish this is to buy an USB to I2C Adapter and connect to A4 (SDA) and A5 (SCL); but maybe I'm wrong.

I have also seen that way: https://gist.github.com/kraftb/8c0bbcc35a9778608d74. Basically to use an intermediate Arduino board.
With SoftwareI2CLibrary you can specify other pins, I haven't tested it with RX and TX.

I would recommend the USB serial interface is fast (2M baud) in perspective to that we are discussing a Arduino with a speed of 16MHz.