Cruz won't do that because he follows the law and respects the Constitutional limits on executive branch power.
Although I don't doubt that he would cancel every executive order Obama has or will make.
I’m convinced the only way the executive branch gets reigned back in is when it strikes at liberals by executive order. It is going to take both sides to agree that the balance of power is out of balance. Some executive orders that are as “offensive” to liberals as obammy has been to us is what it will take to get it done.