Hello...

Yes, you can become a software engineer...

It doesn't rely upon which stream you are on the off chance that you need to progress toward becoming coder. If you see Sundar pichai he himself was a matalargy Engineer and Microsoft's Satya nadella,he was mechanical Engineer. 

Only an insignificant degree won't support you however investing energy with individuals who code, interfacing with them will get you in a more greater spot.

Hope these will be usefull...

All the best!!

Generally in most of the colleges the students of ECE branch are also eligible for sitting in the placement process of software and IT companies although the first preference is always given to the CSE and IT students. Also the ECE students are taught some courses which are a part of CSE branch. Hope this helps.