It sounds like you are using an auto shape and putting a text box inside the
shape and then grouping them. Is that a correct assumption? If you are indeed
using the arrow shape, you should be able to right click on the shape and
choose add text . This way, it will rotate it as one. I am not aware of any
way to allow the move with items that are grouped but I could be mistaken.
Hope this helps.

Thanks Corkey and Suzanne...I appreciate your efforts. Hope somebody out
there can tell me how to rotate a text box, as I could swear that I have done
it before! Just cannot figure out HOW I did it!

I am actually talking to somebody at Microsoft right now...maybe he will
know. I'll report back.

I found the answer, written by Claudette M., in another post. Here is what
she said to do, and it works!

The only way I found to solve the problem of text not rotating along with the
autoshape is to fool Word into believing that the shape is now a picture; you
can rotate pictures. First, on a blank page create your autoshape, insert
your text and do all the formating you need. Then copy the autoshape.  
Return to the document where you want to put the object, and click Edit,
Paste Special, Picture and you've now inserted a "picture" on the page. Grab
the corner and stick it wherever you need it and you can format size, etc.
(as a whole - not individual components of the autoshape) through the format
picture menu.