Yes, using two different methods.

A: Use MapInfo's File>Open menu option, and set the Files of Type to ESRI Shapefile. This option
requires the user to specify a projection, and the file is read-only (it cannot be edited within MapInfo).

B: Use the Universal Translator. This option will pick up the projection information in the shapefile, and
creates a MapInfo table that is editable.

    To use the Universal Translator:

    1/. Within MapInfo navigate to Tools>Universal Translator, open up this tool by clicking on the menu
         item.

    2/. In the Universal Translator dialog, set the Source Format to ESRI Shape.

    3/. Browse to and select the Source Files (Note that you can batch convert by selecting multiple files).

    4/. Set the Destination Format as MapInfo TAB

    5/. Specify the Destination Directory location by browsing.

    6/. Press OK and open the generated MapInfo tab file using the MapInfo File>Open command.

Note: When you import a SHP file colours and linestyles etc are lost. You can retrieve colours by storing these as an RGB code attribute in the SHP file.  These colours can then be re-applied using Discover>Table Utilities>RGB Colourizer, or the Discover>ColourMap tool, which can also batch apply patterns and line styles based on attributes.