It looks like a compression fitting which requires that the tubing be round to make a good seal. The tight bend seems like it has crimped the tubing and probably has broken the seal.
You need a new compression fitting attached to the fridge. If there is play in the copper line, you may be able to remove the fitting, cut the tubing to get to a place where the tubing is not bent and crimped,replace the nut on the tubing and place a new compression ring on the tubing and reseal (with teflon tape on the threads). Make sure that the tubing is going stright down toward the fridge connection and is not bent (like the current one).
If there is not enough play in the tubing, you may need to replace the whole line to the next connector.