Is there a way to store a 64-bit unsigned integer?

What version of Dgraph are you using?

$ dgraph version
 
v21.12.0

I need to store a positive integer value that exceeds the int64 limits.
In the current documentation we do not see any way to create a custom scalar that allows us to define the uint64 format.

Nope, but you could try Custom Tokenizers

https://dgraph.io/docs/query-language/indexing-custom-tokenizers/#sidebar