Is it permissible to swear an oath to abstain from eating a specific food for a week?

There is no harm in swearing an oath to refrain from a permissible act if there is a reason for it and it does not lead to sin or harm. The Prophet, peace and blessings be upon him, and his Companions swore oaths to abandon permissible matters, but they expiated their oaths if they saw something better than them, as he, peace and blessings be upon him, said: "By Allah, if Allah wills, I will not swear an oath and then see something better than it, except that I will expiate my oath and do that which is better." So, if breaking the oath is better, then it is preferable to do so and expiate the oath. There is no harm in persisting in the oath if it does not lead to sin or harm.