You go to Google Maps and Select My Places from the Settings in the lower right corner, then click Create map, and then Create a new map, you will see Import (import data from CSV file or spreadcheet).
By clicking Import, you can upload a CSV file from your computer.
I already tested this, but have no idea how to convert your maps into that CSV file in the first place. There is an option called Export to KML file when you click the folder icon in Create a new map (after creating the map), are those file types the same? Look at the text below from http://EzineArticles.com/5651522.
The file extension KML stores geographic modeling information in an XML format. This information includes lines, polygons, points and image and is used for identifying and labeling overlay textures, locations. These files with KML extension were used originally by a Keyhole mapping software created by Keyhole Incorporated. This company was taken over by Google in 2004. As a result of this acquisition, KML files are now utilized by Google Earth....
The difference between the two types is that CSV files are similar to text ones with the text being more organized while KML is used for storing geographic modeling information.