Running Back to You by Vanessa Williams first appeared on the Israeli foreign-music chart on 29 Oct 1991, entering at #31. It peaked at #31 on 29 Oct 1991. In total it spent 2 weeks on the chart, last charting on 5 Nov 1991.
| Wk | Date | Pos |
|---|---|---|
| 1 | 29 Oct 1991 | 31 |
| 2 | 5 Nov 1991 | 34 |