You should NEVER sign a business document or other contract on behalf of your LLC as owner. This is because when you are serving as the person running or managing the business, you are not doing so in your capacity as an owner of the business but rather in your capacity as a manager or officer of the LLC business.
This is an important concept to get if you care about preserving the limitation of liability protection offered by your limitation of liability company. You never want to do anything that implies that you are doing business in your personal capacity.
One way to evidence that it is the LLC and not you personally that is entering into a legal contract is to make sure you always use a standard title when signing an agreement. The ideal scenario is to have your LLC appoint officers like a President and you can sign agreements as the President of your LLC. For some very simple management structures, if there are no appointed officers and your LLC is member managed, you can sign as Managing Member or if your LLC is manager managed, Manager.
Your legal agreements are very important to your LLC business as they outline the business rights and obligations with other parties. So make sure you take the time to read them properly and have them reviewed by your attorney to make sure you are not legally binding your company to something unintended or unreasonable.