Can outlet circuit ground wires be connected to the panel ground wire?

NEC 250.130(C)(2) Allows connection of ground for replacement receptacles to "Any accessible point on the grounding electrode conductor".

How many wires per connector and size would be subject to the NRTL Listing of the device you are using, which includes the instructions with the device. It seems the smallest wire permitted by the device you show may be larger than the wire you are using.

Actually, you're in luck.

In 2014, they changed NEC to greatly liberalize the rules for retrofitting grounds to ungrounded outlets (of any kind). Before, retrofits were allowed for a few particular places... now they're allowed everywhere.

You can run just a ground wire. (which you normally can't do). It doesn't need to follow the route of the original cable. It needs to be big enough: #14 for 15A breaker. #12 for 20A breaker. #10 for 25-60A breaker. And you can terminate it any of these places:

• The service panel (obviously)
• Any junction box that has a ground wire going back to the panel, if the ground is big enough. It can be on a different circuit, that's fine.
• Any junction box that has (non-flexible) metal conduit back to the service panel. Flexible armored conduit/cable is hit-or-miss whether it is a legal ground wire.
• Any point along the grounding electrode system wires - that is those bare copper wires running between panel and grounding rods/water main/Ufer ground.

You cannot take it to a water pipe, for reasons which should be obvious :)

Right idea, wrong connector

Tapping retrofit equipment grounding conductors (circuit/outlet ground wires) off the grounding electrode conductor (panel ground wire) is permitted by NEC 250.130(C) point 2; however, you can't break the equipment grounding conductor to do so, and more importantly, you need to use the correct connectors for the sizes of wire installed. This is where your plans so far fall short: your split bolt is rated for 8AWG thru 4AWG wires, with no indication of separate tap ratings for an application where smaller conductors are tapped off, such as yours.

As a result, I'd switch out those connectors for ones more suited for your application; my preference would be something like an Ilsco GTT-2-2, but any connector that a) takes the correct wire sizes for both run and tap and b) can be assembled around the existing grounding electrode conductor without breaking it will work. (Note: while putting these junctions in a box could be treated as a Code requirement, it practically can't be as you'd then have to cut and compression splice the GEC in order to retrofit equipment grounding conductors, something I doubt the authors of NEC 250.130(C) intended. Also see NEC 250.10 re: protection of grounding splices from physical damage -- Ilsco makes covers for the GTT series connectors, if that helps.)