It can't be done natively in InDesign. That's a setting that's only available in Acrobat.
If you want to do it in InDesign, you would need my (not free) add-on: https://www.id-extras.com/products/formmagic/
(Actually, for short 1-page forms, there is a free version, so check it out!)
As TaW mentioned, after you've created the form in InDesign and exported as an Interactive PDF you can open the resulting PDF in Acrobat Pro (assuming you have it) and there you can edit the fields – changing the font, the size, colour and alignment (and other things too).
Open the form in Acrobat and go to Tools> Prepare forms. Select the form field you want to edit and right click it to bring up the Field Properties. Under Options, choose Alignment: Center.