A method is provided for making a fiber wire having a fiber bundle core and a polymer jacket. The method includes rotating a spool of fiber bundle about a first rotational axis to progressively unwind the fiber bundle from the spool. The fiber bundle includes a plurality of continuous synthetic fiber filaments. While the spool is rotated about the first rotational axis, the spool is simultaneously rotated about a second rotational axis to thereby twist the unwound fiber bundle about its longitudinal axis. The method further includes coating the twisted fiber bundle with a molten polymer, and permitting the molten polymer to cool to define a flexible outer jacket that encapsulates the twisted fiber bundle.