Can I connect an electronic air cleaner to the 24v terminals of my furnace?
Generally, yes, R and C are the 24 volt and common terminals of the transformer.

However, you have to make sure you do not draw more current than the transformer can handle. These things are usually rated in volt-amps. If your furnace, air handler and air conditioning compressor are marked with their ratings, you can tell how much power you can spare. Don't exceed 80% of the rated capacity of your transformer.

As an alternative, you can mount the transformer that came with your air cleaner in/on your air handler. Locate the existing transformer and you can wire the new one in to the same 120 volt lines.