The first thing I will say is that tape is NOT an option. It will eventually lose it's ability to hold and it will leak again.
There are a couple of options to repairing your leak. The first, assuming that the water line is plastic, is to actually cut the water line at the spot where the water line has the hole. At that point you would use a 1/4" X 1/4" compression coupling,specify at time of purchase of coupling that it is for a plastic water line this fitting will come with 2 brass inserts and 2 plastic ferrules, they look like rings, you can not use a coupling made for copper tubing because the brass ferrules will cut in to the plastic water line and leak. This repair is based upon your water line being plastic not copper. This procedure can be duplicated if it's copper, only you would use a coupling for copper not plastic. The second, and more preferable, way would be to replace the water line from valve to solenoid valve of unit with a 1/4" copper water line. The replacement of the water line is the better way because there is a reason that there is a leak, whether it's age or fatigue of the water line, either way a leak could develop in another part of the water line and rather than risk another leak it would be best to replace the whole line with a new 1/4" copper water line.