I'm assuming you mean +/- 6 V from the body of your question, rather than +/- 5 V from the title.
There are a number of ways to achieve this, depending on both your budget, and power budget. You probably don't need a huge amount of power for this application, so the easiest route is probably TI's TLE2426 rail splitter IC.
A second option is something like the following, the Virtual Ground node isn't really 0 V, it's +6 above the GND node, but you treat it as your 'virtual ground' and the actual ground node becomes -6 V.
simulate this circuit – Schematic created using CircuitLab
If you need to sink and source more current than the opamp can supply you can add a buffer (such as TI's BUF 634) which is an expensive option, or put a push pull stage within the feedback loop.
You could also AC couple and bias your signal to +6 V so you don't need to worry about the negative supply.