In BarcodeMaker, the caret character is used to escape ascii numbers if you want to encode a special character. For example, if you wanted to encode a line break, ascii character number 10, you would put "^010" into your data and a line break would be inserted.
So what if you want to actually encode the caret character itself?
If you want to encode a caret character, you can't put the caret character in your data directly, because BarcodeMaker expects three digits to always follow. Instead, you have to put ^094 (94 is the ascii number for a caret).
To get DataLinker to deal with this without modifying your data, you could use the regex find and regex replace options in the Field Options dialog, once a barcode type is chosen.
Regex find:
\^
Regex replace:
^094
The caret in the find area needs a backslash because carats are special codes in regular expressions.