They make "taps" specifically for that purpose - you can get them at home depot/lowes or probably any plumbing store.
They clamp on to an existing water line and have a sharp pin inside. You attach a vinyl or flexible copper line to it and run it through the floor to the fridge. Then you crank handle on the valve down and the pin punctures the copper water line and lets water into the valve.
When I did mine, I was a bit worried it would leak at first (they just look like something that wouldn't seal well) but haven't had any problems with it for well over a year now.
I'd use a small tubing cutter to cut tidy/clean ends on both ends of the 1/4" copper pipe ...
... cutting off whatever portions of the 1/4" copper pipe are kinked or deformed. I'd then slip on a compression fitting called a 'union' ...
... which requires tightening with a pair of wrenches. Wikipedia has a general article on compression fittings here. You-tube hosts a concise 3 minute how-to video regarding installing compression fittings on plastic or copper pipe. The copper tubing portion of the demo starts at 1:45 ...
http://www.youtube.com/watch?v=eQGL8MBLlaE
Small tubing cutters such as the one pictured above will cut diameters 1/4", 1/2" and 3/4" and anything in between. The small size of that cutter design makes it excellent for tight confines. It would be the first one I'd buy for my tool box. You could also use a medium size cutter, such as the one used in this 90 second tutorial ...
http://www.youtube.com/watch?v=nLB3MomrXd0
The small cutter works in the same way. There are two main points to keep in mind when using either of these tubing cutters ...
1) Tighten the cutter only a little bit each time, making a number of light scores around the pipe instead of several deep ones.
2) The cutter wheel needs to continually track in the previous score, so keep a close eye on the score and make sure the score is not spiraling along the length of the 1/4" copper pipe, which can happen if the pipe is bent or deformed in the area where the cutter is being used.
After the cuts are completed, the cut ends of the 1/4" pipe need to be very close to circular (for example, not deformed into an oval). If they are not circular, then even if the ferrules can be forced onto the 1/4" copper pipe, the fitting will leak. If the ferrules do not slip on easily, it might be due to the ends of the 1/4" pipe being out-of-round, or (unlikely) due to defective ferrules. Using a tubing cutter will help ensure the cut ends of the 1/4" copper pipe are circular.
Alternatively, a hacksaw (or similar) can be used to cut clean ends on the 1/4" pipe. This will likely result in ends with sharp edges and a burr. Remove these with sandpaper. Clean ends will allow the ferrules slip on without gauging, which would lead to a leak. A fine-toothed file can be used instead of sandpaper, but the copper dust/shavings will most likely clog the teeth of the file.
Here is a 7 minute how-to video from England regarding leaks at compression fittings:
http://www.youtube.com/watch?v=aez4ctMtbuI
Best Answer
This is an Drop Elbow (upside down for your use), most commonly used for wall penetrations...showerhead arms, tub faucets, washing machine supplies, etc. I don't know of any other types that you'd actually screw to the floor & haven't ever seen one.
Presuming your hole is tight to the wall or baseboard, you might be able to attach this to your wall or baseboard with either a direct connect flexible line or a single compression fitting. Anything more would likely get crushed by the fridge. But a screw in elbow fitting to convert to vertical may work for your situation. However, elevating the fridge's tube connection that's already set-out much may put it in threat of being crushed, so be careful & test it out gently.
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Male solder-on or sweat-on. My preferred floor lock-in fitting. Threads are exposed for thread inspection, easy Teflon taping, more precise leak detection, female reducing adapters are more common & flexible lines come with direct attachment ends.
Female solder-on or sweat-on. Nothing really wrong with this. I just don't find much of a selection to accommodate it in the big stores.
All three would be first soldered onto the pipe you drop in the floor. It's ill-advised to feed a pipe up & then later solder on a fitting that's close to a wall, especially when so easily avoidable.
Your pipe or elbow beneath the floor would prevent or limit vertical movement & a hole drilled for the pipe diameter instead of for the fitting's shoulder would raise the fitting for easier future flexible line replacements & stop downward movement to avoid stressing of the piping beneath the floor.