In recent years, integrated lithium niobate (LN) chips have been widely used for developing a variety of photonic devices, such as high-speed electro-optical (EO) modulators and frequency comb generators. A major challenge for their practical applications is the high coupling loss between micrometer-scale LN waveguides and optical fibers. Lensed fibers and special taper structures are commonly used to tackle the coupling issue. However, in some situations, these approaches may increase the overall complexity and cost of design, fabrication, and alignment. Here, we propose using the self-written waveguide (SWW), an optical waveguide induced by light irradiation, to cope with this coupling issue. The approach can apply in connecting a single-mode fiber (SMF) to any waveguide surface in principle, even with a large mode-field mismatch, significantly alleviating the tight alignment requirements typically needed for end-fire coupling into integrated waveguides. Our study demonstrates that the coupling loss between a SMF with a mode-field diameter (MFD) of 4.4 µm and a sub-micrometer LN rib waveguide could be dramatically reduced from an initial value of -14.27 dB to -5.61 dB, after double-side irradiated SWW formation. Our proposed approach offers a potential solution for achieving a cost-effective and flexible fiber-to-LN chip optical interconnect.