Adding content type field value to a taxonomy term?
If you are using Select (or Other) module and it does not specifically need to be a taxonomy term, there is an option for exactly this:

On the field edit page, the &quot;Other value as default value&quot; allows you
to select how other will be handled:

Add the values to the other textfield-&gt; store the value but don't
change the list

Append the values to the current list-&gt; store the
value and add to the list attached to the node/user/entity

Append the values to the available options-&gt; store the value and add the value to
the list so that it can be selected on other nodes/users/entities

Ignore the values-&gt; do not store the value



EDIT (courtesy of DuaelFr)
You will need the 7.x-3.x-dev version to be able to use this module on a Taxonomy Reference Widget.