I am using ArcGIS 10.2.1 for Desktop and have access to ArcGIS Online for organization.
Is there any way I can log into AGO for organization from ArcMap?
Under the File menu, see the Sign In option:
Once you've signed in, you will be able to add data to ArcMap from ArcGIS Online - rather than hitting the + of the Add Data button, use the dropdown beside it:
You will also see My Hosted Services in the ArcCatalog window: