Raster datasets in ArcGIS do not contain strings for each cell, natively, the values in the raster are numbers. When there is a string value for a cell it is stored in a raster attribute table related to each value. (Only integer rasters can have such a table.)
I disagree, I believe Steve Lynch is right on (as usual, Hi Steve) in suggesting Combine(): this is a more general solution as you could then a build a Calculate Field expression to populate a string field in the raster table with something that you want like "0207". One could do other encodings (to strings or numbers) by using a different Calculate Field expression.
1. Combine("ras1", "ras2")
The output will raster table will have two fields, RAS1 and RAS2, with a row for every unique combination (not every cell) and a COUNT of how many had that combination.
2. Add Field, "RCODE", "TEXT"
3. Calculate Field Python expression: "{:02}{:02}".format(!RAS1!, !RAS2!)
The RCODE field will be set to "0207" if RAS1=2 and RAS2=7 for that row.