Is this possible?

Hi everyone,
I'm quite new to arduino so I was wondering whether it is possible to save code as a text file to an sd card, and then use a sketch uploaded to the board to read the file and then execute the code.

Thanks in advance.

Without using a compiler and linker? No.

you can write an interpreter for the code that reads a command from SD and then executes it. Then it goes to the next line.
Not trivial to implement.

have a look at bitlash - http://bitlash.net/wiki/start - to get started