Obviously, the RPi can be used to mine Bitcoins on the CPU, but this would be very slow.
Is it possible to use the GPU to mine Bitcoins?
Until 2014, the GPU firmware was closed source. OpenCL was not supported by the Pi until the VC4CL project, which has started to implement OpenCL on the VideoCore IV GPU used by all Pi models. The project's progress is also discussed on the Raspberry Pi Forums.
See Can I use the GPU for calculations? for the state of the GPU as of 2012, but much has changed since then.
As the VC4CL project is relatively new and OpenCL support isn't mature, there don't appear to be any attempts to mine Bitcoin on a Pi yet. It may be possible with a great deal of reverse engineering, but that most likely wouldn't be economically viable.
The general consensus is that even if OpenCL were supported by the GPU, it would still achieve a poor hash rate because it only has one or two cores. Fast hash rates are achieved by many modern GPUs because they have several hundred cores which can run together in parallel.
The best thing to do is to head over to: Mining hardware comparison - Bitcoin, find yourself a dedicated hardware and then hook it up to Raspberry Pi)