Unfortunately, ArcGIS does not support the viewing or conversion of cgm files. Neither does the Data Interoperability Extension or Safe Software's FME product.
You'll need to use a third-party application, such as Larson's VisEx Professional, to convert the cgm to a tiff (the free VisEx viewer does not have the capability to convert between different formats). The tiff can then be read or converted to vector format using tools within ArcGIS.
Although I haven't personally worked with Petrel myself, please take a look at the forum thread below which offers a few suggestions about this process.
This allows you to export and import various culture, interpretation, seismic and well data formats to and from ArcGIS, notably for Petrel, Landmark and KINGDOM.
