Trapped atomic ions are among the most promising architectures for realizing a universal quantum computer. Universal sets of gate operations are available and proof-of-principle quantum computation and quantum simulation have been demonstrated with high precision. The current focus in this field is to realize fast entangling gates in large systems. Normally collective motional modes are crucial for entangling gates, while recently Rydberg interaction has become a new degree of freedom in trapped ion systems and has been used to achieve a sub-microsecond entangling gate in a two-ion crystal. In this Letter, we report the Rydberg interaction gate with the same gate time (700 ns) in a 12-ion crystal without using motional ground state cooling by employing a motion-insensitive, strongly-interacting Rydberg state. Thus we confirm that this Rydberg interaction gate is highly independent of ion number and temperature, demonstrating its potential for speeding up and scaling up trapped ion quantum computers and simulators.