I am trying to create a slope map. I have many contour elevation files. I tried to use the slope tool in ArcToolbox, but it calls for raster files and I'm working with vector data.
You first need to make a raster DEM from your contours. That requires the Spatial Analyst extension, and uses the Topo to Raster tool (Spatial Analyst | Interpolation toolbox). That elevation raster can then be used as the input for the Slope tool.
Note that since this is an interpolation process, it is estimating the elevation values between the contour lines. That's simply a source of possible error to be aware of in subsequent analyses and/or interpretation of results, however.
You can create a TIN from your contours, then convert the TIN to a raster, before calculating the slope, tutorial here https://www.youtube.com/watch?v=ZxRu7nAbDAs