The only way you'll accomplish that is if you have a ring custom made. When custom making a ring, a jewelry maker makes it out of wax, puts it in plaster to harden, melts the wax out of the cast that forms and then fills the cast with melted gold or silver or whatever metal.
The only other way you might get that gold incorporated would be if you bought a ring that was too small and needed to be enlarged. In that case, a jewelry maker could use the gold to cast whatever insert they would use to solder in to the bottom of the band, but I can't see any jewerly maker doing that because the gold you have is unrefined -- and if it's not, if it's 24K gold, then it's far too soft to use for the bottom of ring band and the process of making it into an alloy to be an 18K, or 14K, or 10K gold that matches the existing is beyond what jewelry makers do. Even if they could, the process would be so involved, it'd end up costing you more than a custom-made ring.
Basically, the only way that's happening is if you have a ring custom made by a jewelry maker and those gold pieces mixed in with the gold they use to cast that custom-made ring.