A calcium build-up in copper pipes is a rarity, though it is possible with extremely high levels of calcium. If this happens, you'll need to install a water softener to treat the water. This will not only save your pipes, but also your washing machine, dishwasher and toilets. As far as removing the calcium from the inside of the copper pipes, there is nothing you can put into the pipes that you would want to drink later. No governmental agency will allow plumbers to treat the inside of copper pipes because of the hazards involved.
You could use vinegar in the pipes, but it would take a lot of vinegar and you would have to leave it in the pipes at least 24 hours. You would have to remove all of the water in the pipes and replace it with vinegar. Vinegar dissolves calcium and minerals. Then you would have to flush your pipes. The vinegar taste may be in the pipes for some time afterwards, but it is completely harmless.
A better solution is to simply replace the pipes with PEX plastic pipes. Plastic is completely resistant to any mineral build-up and provides higher pressures and water flow rates than copper pipe. A ROTO-ROOTER plumber can evaluate your pipes and give you some options.