If you are interested in Facebook sign up, you can do that from your mobile also. To sign up for Facebook.com you can enter a mobile number of your choice. From your mobile device Go to www.Facebook.com or open the Facebook app and find the sign up link under the log in section. After that enter your real name and birthday. Now enter your mobile number and choose a password of your choice. Finally click Sign Up.
After you sign up for Facebook using a mobile number it is a good option to add an email address to your account as well. If you have created a Facebook.com account using your email address you can add a mobile number to your account once you complete the Facebook sign up process.