Placing text inside a shape

To import the contents of a text file into a shape in Illustrator, you must first convert the shape into Area Text by clicking on it with the Type tool, as described in Reply #1.

Then, to import text from a source document into an existing text context, you must make a text editing selection (usually a caret) instead of selecting the whole object with the Select tool. Once you have a text editing selection, the File>Place command acts like opening the text file, copying the text, making that same text selection, and doing Paste.

If the text is being imported but is not visible, it may have a lot of formatting white space at the beginning that makes all the regular characters go beyond the end of the space available. Is the file just a plain .txt file, or is it some kind of formatted text (.rtf, .doc, .dxf, etc.)?

File...Place is for importing files. To "place" text inside a shape, select the "Area Type Tool" in the toolbox, click a shape with it and start typing.