We present deep surface photometry of a very faint, giant arc-loop feature in the halo of the nearby spiral galaxy NGC 5055 (M63) that is consistent with being a part of a stellar stream resulting from the disruption of a dwarf satellite galaxy. This faint feature was first detected in early photographic studies by van der Kruit; more recently, in the study of Martínez-Delgado and as presented in this work, from the loop has been realized to be the result of a recent minor merger through evidence obtained by wide-field, deep images taken with a telescope of only 0.16 m aperture. The stellar stream is clearly confirmed in additional deep images taken with the 0.5 m telescope of the BlackBird Remote Observatory and the 0.8 m telescope of the McDonald Observatory. This low surface brightness (μ R ≈ 26 mag arcsec-2) arc-like structure around the disk of the galaxy extends 14farcm0 (~29 kpc projected) from its center, with a projected width of 1farcm6 (~3.3 kpc). The stream's morphology is consistent with that of the visible part of a giant, "great-circle" type stellar stream originating from the recent accretion of a ~108 M sun dwarf satellite in the last few Gyr. The progenitor satellite's current position and final fate are not conclusive from our data. The color of the stream's stars is consistent with dwarfs in the Local Group and is similar to the outer faint regions of M63's disk and stellar halo. From our photometric study, we detect other low surface brightness "plumes;" some of these may be extended spiral features related to the galaxy's complex spiral structure, and others may be tidal debris associated with the disruption of the galaxy's outer stellar disk as a result of the accretion event. We are able to differentiate between features related to the tidal stream and faint, blue extended features in the outskirts of the galaxy's disk previously detected by the Galaxy Evolution Explorer satellite. With its highly warped H I gaseous disk (~20°), M63 represents one of the several examples of an isolated spiral galaxy with a warped disk showing recently discovered strong evidence of an ongoing minor merger. This paper includes data taken at The McDonald Observatory of The University of Texas at Austin.