Can a magnetic wire be used to extend/strengthen the signal coverage of a cellphone?
This will do absolutely nothing.  What you could consider doing is picking up a pair of antennas and a length of coax cable for the correct cell band.  I think that would be around 800 MHz.  It should be possible to get a couple of cheap 800 MHz antennas and maybe 20 feet of coax with the proper connectors for around $20 or $30.  If you know where the local cell tower is, you could consider getting a log-periodic or other directional antenna for the external antenna and mount it so that it points at the cell tower.  Note that this may not help very much; it's going to be more useful for, say, a basement that has thick concrete walls where reception inside is zilch and reception outside is very good.  If reception outside is only mediocre, then you may have to get a repeater or a femtocell.