Adding a Twitter button is quite easy as you can simply create a link with your URL-encoded quote added to your link’s href attribute. Obviously, you need to update this every time you generate a new quote.
The link looks like this:
https://twitter.com/intent/tweet?text=YOUR+QUOTE+HERE
It seems you use Bootstrap so a simple button looks like this:
<a href="https://twitter.com/intent/tweet?text=YOUR+QUOTE+HERE"
class="btn btn-info btn-lg"
target="_blank">Tweet It!</a>
You can find more info about it at Guides | Docs | Twitter Developer Platform
Consistent height of what? You can use the height property…