I find the question a little confused:
Either you consider your C code to be in support of higher-level R functions that you can test at the R (as you seem to have done)
Or you consider your C code to be more standalone, in which case you could use one of a bazillion unit testing frameworks for C.
Many of the packages using Rcpp also use extensive unit testing, either via RUnit, or via testthat. You could look at that. I generally test at the R function level, which often implies a test of the underlying C++ function.