Yes, nervousness raises your heart rate. When you are stressed, fearful, or anxious, a signal is sent to a part of your brain called the amygdala. From the amygdala, it triggers the sympathetic nervous system.
The sympathetic nervous system is a part of your autonomic nervous system, which does as the name implies- it is ‘automatic’ and controls the organs in your body that are not under conscious control- it is involuntary. The autonomic nervous system also includes the parasympathetic nervous system, which deals with slowing down your body, growing your body, and reproduction. On the other hand, the sympathetic nervous system is involved with the fight or flight response, which help you deal with dangerous situations and helps you to survive.
The sympathetic nervous system is connected via nerves which attach to and control different organs in the body, such as the heart, lungs, skeletal muscles, and pupils. When the sympathetic nervous system is activated, it increases your heart rate, dilates your pupils, tenses your muscles, and opens up the air sacs in your lungs.
In addition to direct neural connections to organs, the sympathetic nervous system also activates the adrenal glands (which sit on top of the kidneys) to release adrenaline into bloodstream. The adrenaline then travels to the heart to increase heart rate, and also travels to other body organs. This all helps to prepare to either fight the danger, or run from it.
So when you are nervous, you set off the amygdala, which then activates the sympathetic nervous system. The sympathetic nervous system then directly increases the heart rate via the nerves, and also increases heart rate by activating the adrenal glands to release adrenaline, which then travels to the heart via the bloodstream and also increases heart rate. So both direct sympathetic nerve stimulation and adrenaline in the bloodstream reaching the heart increases the heart rate.