Does the r4 work on the dsi?

This is not a simple answer... let me explain:

If you have updated your DSi to version 4.0 then you CANNOT because this update will have blocked cards such as R4 etc.

If you HAVE NOT updated your DSi to version 4.0 then there are two explanations.

The R4 card will not work because they only work on NDS/NDSLs.

However, you can use cards built for DSi like the AceCard and the DSTTI card.