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She found a part-time job so she could study at college.
Literal
She [topic-は] college [at-で] can-study [so-that-ように] part-time-job [object-を] found.
Two notable points. ~ように (purpose) is paired here with a potential verb 勉強できる ('can study') to express 'so that one can X.' This is the standard pattern: with non-volitional or potential verbs, ~ように means 'so that.' アルバイト is a katakana loanword from German Arbeit ('work') — borrowed during the Meiji era when German influence was strong, and now fully naturalized in Japanese as the everyday word for a part-time job. The casual abbreviation is バイト.