@keagan-allan gave two great options.
Assuming you are working in arcMap: If you want to add area using Model Builder or an arcPy script, you can use the "Add Geometry Attributes" geoprocessing tool. See: http://desktop.arcgis.com/en/arcmap/latest/tools/data-management-toolbox/add-geometry-attributes.htm
The "Add Geometry Attributes" tool allows you to define the units for the area. This is helpful if you want to calculate the area using units that differ from the coordinate system of the input features. For example, the layer uses meters as the liner unit, but you'd like to calculate the area in Acres. You could always use the default and then convert the units using the field calculator later, but this saves you a step. If you do this, be sure to record what units your area field uses in your meta-data.
Note from the documentation:
If the fields already exist in the input features, the values in
those fields will be overwritten.