We achieve submicrometer precision in the integration of micro-optics with surface electrode ion traps. The high-precision alignment is accomplished using off-axis linear Fresnel zone plates (FZPs). Four pairs of FZPs are fabricated on the optics chip that contains the high numerical aperture microlens, a diffractive optical element (DOE). The four pairs of FZPs enable alignment in six translational and rotational degrees of freedom. Four corresponding alignment rulers are etched in the top metal layer of the ion trap, enabling quantification of misalignment. The integration of optics for efficient light delivery and the collection of fluorescence from trapped ions are key to achieving scalability in quantum information processing. An accurate and precise approach to the integration of DOEs advances the scalability of surface electrode ion traps and many other hybrid microsystems.