Facebook has some frustratingly limited options when it comes to sharing high quality photos. Fortunately, it's getting better. Android users can now upload HD photos directly from the mobile app.
According to Android Police, Facebook is currently rolling out the option as a server-side switch (meaning that you won't see it just because you update the Facebook app). To turn on HD uploads, head to App Settings in Facebook and toggle the Upload HD Photos switch as seen above.
Keep in mind, this won't upload full-res versions of your photos. Facebook's high quality pictures max out around 2048px wide. Your pictures will also be compressed to a degree, but the HD uploads should be an improvement over what you're used to.