Sure, you already can and we have had solutions such as Gigabyte's i-RAM, released in 2005, for some time. But these products required an uninterrupted power supply that caters to DRAM's volatile characteristics. However, there is a new product, a DDR3 DIMM offered by AgigA Tech that is created as a non-volatile DIMM (NVDIMM).
The product uses an integrated controller to transfer the contents in the DRAM to also integrated NAND Flash. The briefly required power supply is provided capacitors, which do not require a separate battery. To recharge the capacitors, only "a few seconds" of regular power supply to the DIMM are required. AgigA Tech says that the data retention time in the DIMM is a remarkable 10 years.
At this time, the DIMMs are available in ample numbers as well as 1 GB, 2GB and 4GB capacities. There was no information when these DIMMS will become generally available and how much they will cost. However, do not expect these chips to be affordable for your desktop system anytime soon; AgigaTech said it is targeting RAID storage, servers, data deduplication, workstations, embedded systems, communications/networking, as well as industrial/medical as initial application fields.