Answer:
Yes
Explanation: Electric and magnetic field are known to be inter-related, this implies that for any current carrying conductor there is a resulting magnetic field around the wire ( for example a current carrying conductor deflects a compass) and a magnetic field has been known to produce some amount current based on the<em> </em>principle of electromagnetic induction by Micheal Faraday.
The strength of magnetic field generated by a current carrying conductor is given by Bio-Savart law (purely mathematical) which is
B =
B= strength of magnetic field
I =current on conductor
r = distance on any point of the conductor relative to it center
If a current carrying could generate this magnitude of magnetic field, thus this magnetic field has the ability to interact (exert a force on any magnetic material) with any other magnetic material including a magnet.
Yes, a current carrying conductor can exert a force on a magnetic field