I need to re-route my house ground wire in my basement,due to remodeling. About 5 years ago, I had the electrical bumped up to 200 amps because of necessity. My panel is in the garage, & the water inlet is in the opposite end of the house, about 100 feet worth of ground wire away. It is stapled to the ceiling joists, so I would like to drill holes in the joists & put up a ceiling.There are 2 grounding rods 6 feet apart outside the garage door, installed at the time of new electrical.

While often done, stapling cables or wiring to the bottom of joists is not allowed. Suppose to be stapled to a runner board that is attached to the bottom of the joists.

Sure you can pass the wire through holes drilled through the joist. Just do not drill through the center third of the span of the joist.

The wire going to the ground rods should be no smaller than # 6, however the wire going to the water line can be no smaller than #4, for a 200 amp service.

Be sure the connection of grounding wire at the water line is no farther that five feet from the point of entrance into the home. If you have a water meter, connect the ground wire on both sides of the meter, to jump out the meter.

Is the water entrance pipe metallic where it enters the house? Or is it poly like most wells have?

Is the water entrance pipe metallic where it enters the house? Or is it poly like most wells have?
Reason I ask is because if it is not metallic you do not have to run all the way back to the entrance. You can run to the nearest accessible cold water pipe.