You would need two adapter cables (one at each end of the SATA cable) so in cost terms that doesn't make sense. Just buy an eSATA cable.
My computer does not have an esata outlet to hook into. I was thinking of an esata card and cable, but thought that if I could use the spare sata cable I might get away with that. I think I've seen a cable advertised that has esata at one end and a connector for the internal sata cable (normally used for internal hard drive). It seems like it would work, but I'm not savvy enough to really know.