Yes, you can touch your wife during her period. According to available information, there's no need to avoid sexual activity during menstruation unless it troubles either partner.
Intimacy and Periods
- Safety: Period sex is safe.
- Benefits: It can even have benefits.
- Messiness: It can be a bit messy.
In conclusion, physical contact, including touching and sexual activity, is permissible and safe during menstruation, provided both partners are comfortable.