Well, there are two approaches:
1. Directional network model. If you want the actual underlying network model to be correct in terms of direction, then you need to pre-define “source” and “target” columns. You can’t import a mix of and expect Cytoscape to know which is source based on an arbitrary symbol in a third column.
2. Directional network appearance. If you don’t care what the actual model is and only need the visualization or appearance of the network be directed, then you can take the same file you’ve already imported and use the column of direction symbols to map discretely to source and target arrowhead types. See manual
http://manual.cytoscape.org/en/stable/Styles.html#introduction-to-style
The second approach can produce networks with arrows pointing in the direction you want, but know that network functions that rely on directness (like in-degree/out-degree calculations) use the model, not the visual style and will be wrong if you take this approach.