Can I travel to Gibraltar with a Schengen visa?

It should not be possible.

1. The countries included in the Schengen Area are: Austria, Belgium, Denmark, Finland, France, Germany, Iceland, Italy, Greece, Luxembourg, the Netherlands, Norway, Portugal, Spain, Sweden, Hungary, the Czech Republic, Slovakia, Slovenia, Poland, Estonia, Latvia, Lithuania, Malta, Switzerland and Liechtenstein, the above list of Eurozone and Schengen countries is as of January 1, 2009.

2. Gibraltar is a British overseas territory, and its supreme head of state is Queen Elizabeth II. The British royal family appoints the governor and garrison commander to perform local duties on its behalf and is responsible for foreign affairs, defense and public security. The UK is responsible for Gibraltar's defence, foreign affairs, law and order and financial stability. Therefore, it belongs to the UK and is not included in the Schengen area.

If Gibraltar has any additional exemption regulations, it is recommended to check directly on the official website of the Gibraltar Tourism Bureau. You can definitely find it by searching for keywords on Google.