The browsers I use most -- Safari on iPhone and iPad -- do not allow this. The only way to increase font size is to zoom the entire page, which often results in lines that are too wide for the screen.

And a growing number of websites take deliberate steps to prevent any zooming on the page. I can't understand why any designer thinks this is helpful.

At least iOS Safari has "reader" mode now, which does what I wish most websites would do: throw away all of the CSS, and render the page as a plain list of H1's and P's.