Yes, coffee can cause nervousness and anxiety. The key ingredient in coffee that causes nervousness is caffeine. One cup of coffee has 100mg of caffeine. If you ingest more than 250mg of caffeine on a daily basis, then you can develop caffeinism, which has characteristic symptoms of anxiety, nervousness, irritability, restlessness, tremulousness, rapid breathing, palpitation, muscle twitching, flushing, sleep problems, and gastrointestinal problems (Victor et al., 1981). So if you drink more than 2 cups of coffee on a daily basis, then you are at risk for developing caffeinism.
And if you drink too much coffee and abruptly stop drinking coffee, then you can get caffeine withdrawal symptoms characterized by anxiety, irritability, and headaches.
Reference:
Somatic manifestations of caffeinism. Victor BS, Lubetsky M, Greden JF. J Clin Psychiatry. 1981 May;42(5):185-8.