We present a new method to form liquid-core optofluidic waveguides inside hydrophobic silica aerogels. Due to their unique material properties, aerogels are very attractive for a wide variety of applications; however, it is very challenging to process them with traditional methods such as milling, drilling, or cutting because of their fragile structure. Therefore, there is a need to develop alternative processes for formation of complex structures within the aerogels without damaging the material. In our study, we used focused femtosecond laser pulses for high-precision ablation of hydrophobic silica aerogels. During the ablation, we directed the laser beam with a galvo-mirror system and, subsequently, focused the beam through a scanning lens on the surface of bulk aerogel which was placed on a three-axis translation stage. We succeeded in obtaining high-quality linear microchannels inside aerogel monoliths by synchronizing the motion of the galvo-mirror scanner and the translation stage. Upon ablation, we created multimode liquid-core optical waveguides by filling the empty channels inside low-refractive index aerogel blocks with high-refractive index ethylene glycol. In order to demonstrate light guiding and measure optical attenuation of these waveguides, we coupled light into the waveguides with an optical fiber and measured the intensity of transmitted light as a function of the propagation distance inside the channel. The measured propagation losses of 9.9 dB/cm demonstrate the potential of aerogel-based waveguides for efficient routing of light in optofluidic lightwave circuits.