You would have to use some media queries to manage the mobile version.
I gather from what you are writing that you are using free-form landing pages ?
You should probably consider moving to guided (natively responsive) landing page templates. In these Guided LP, the form will be natively responsive.
Having had a similar issue in the past it seems like the button's default 'padding-left' may be the problem (but it is hard to say without seeing the code / page).
If you can login to Marketo and look at the form, is the button centered within the editor?
If so, drag it to the left to remove a system default styling
^ it looks like it's centered, but it's really adding a padding-left CSS style. Pull it to the left to undo this and rely on your CSS (which is probably working)
Hope it helps!
Better make a small change to the form CSS, if yiou want my take
Nothing wrong with a media query to fix it. I used to do it this way as well before figuring out what was adding 'padding-left: 120px;' which is the issue.
Option 1: remove the default CSS so that the button centers how it should (my suggestion)
Option 2: write more CSS to then undo Marketo's bad CSS (Gregoire's solution)
hope it helps!