Demo
https://www.dropbox.com/s/5k5cvfxlgumrb69/AppDemoHttpGet.zipAlready compiled project for arm7, has OpenSSL libs compiled by me.
If you need 64bit or newer versions download OpenSSL libs from @josh link.
EDIT:
There are some problems with the demo.
After http.UserAgent := UserAgent; add line
http.Headers.Append('content-type: text/html; charset=UTF-8');
After ShowMessage('Too many redirects!'); add
Replace jTextView1.Append(Utf8EscapeControlChars(response)); with
jTextView1.Append(response);