Yes, panic attacks can raise your blood pressure temporarily. When you have a panic attack, you have set-off the fight or flight response. When the fight or flight response is triggered by anxiety, the amygdala is activated, which then activates the sympathetic nervous system. The sympathetic nervous system innervates the heart and blood vessels, which increases the heart rate, makes the heart beat stronger, and constricts blood vessels, resulting in increased blood pressure.
Blood pressure is further increased with adrenaline that is released from the adrenal medulla, which is activated by the sympathetic nervous system. The adrenaline that is released into the bloodstream then travels to the heart and blood vessels, which also increases heart rate, increases contraction of the heart, and constricts blood vessels. This also results in further increase of the blood pressure.
Once the panic attack is over, then the fight or flight response subsides, and the blood pressure subsequently drops.