Narrow pentaquark states may arise in constituent quark models and such states may be studied precisely at electron accelerators. The photoproduction of the $\Theta^+(1540)$ resonance on the nucleon, through $K$ and $K^*$ Regge exchanges is analyzed. The size of the cross sections for the $\gamma n \to K^- \Theta^+$ and $\gamma p \to \bar K^0 \Theta^+$ reactions are compared. The model allows us to estimate the cross sections corresponding to a given upper bound on the width of the $\Theta^+$. Furthermore, the cross sections sensitivity to the spin-parity assignments $J^P = \frac{1}{2}^\pm$ and $\frac{3}{2}^\pm$ for the $\Theta^+$ resonance is investigated. The photon asymmetry is found to display a pronounced sensitivity to the parity of the $\Theta^+$, making it a very promising observable for determining the quantum numbers of the $\Theta^+$ resonance. This analysis is relevant to a planned Hall A experiment at JLab that will provide the most definitive statement to date on the existence of the $\Theta^+$.
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