From my review of the Architecture Merit Badge, it appears that drafting scaled drawings are just a part of obtaining the badge. Regardless, I would suggest that doing it be hand may be easier than learning a free CAD software. Of course, with hand drafting, you would need a drawing board, t-square, scale, triangle, and drafting pencils.
Measure a room such as one where you live or where your troop meets. Make an accurately scaled drawing of the room's floor plan showing walls, doors, closets, windows, and any built-in furniture or cabinets. Neatly label your drawing with the following: your name, the date, what room you drew, and the scale of the drawing. (Drawing scale: ¼ inch = 1 foot)
With that said, I will be honest - I am NOT an expert on software but from a simple Google search, found the following that might be helpful. I do not offer an opinion on one over the other as some are Windows based while others are cross platform.
Further, if your son is interested in architecture, I suggest he obtain Becoming an Architect, 2nd ed. (see attached).
As well, visit the website - http://www.archcareers.org --