Can I get a Michigan tax ID if I live in Texas?
I presume your question relates to a business tax ID, specifically Sales Tax ID in Michigan for your business (probably one registered in Texas).
If that is correct than yes, you can generally register to collect a sales tax in Michigan, assuming that you are required to do so. You will be required to do so if you plan to sell taxable products/services and have what is called "nexus" in Michigan, in other words your business has or uses related assets in that state (a notable example of nexus is use of Amazon FBA services to fulfill your product in states where Amazon has its warehouses).
Keep in mind, if you establish physical presence in the state other than the state of formation you will be required to register your company as Foreign Entity (in addition to obtaining a sales tax ID if you sell taxable products or services in retail in that state).