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Is this a compound or complex sentence? 
I think it might be compound because it has “so”.

My car battery died, so I called to have it towed for repairs.

It is a compound sentence.

From study.com Link:

"Definition

A compound sentence is a sentence that has at least two independent clauses joined by a comma, semicolon or conjunction. An independent clause is a clause that has a subject and verb and forms a complete thought.

An example of a compound sentence is, 'This house is too expensive, and that house is too small.' This sentence is a compound sentence because it has two independent clauses, 'This house is too expensive' and 'that house is too small' separated by a comma and the conjunction 'and.'

Compound Sentences and Meaning
When independent clauses are joined with coordinators (also called coordinating conjunctions) commas and semicolons, they do more than just join the clauses. They add meaning and flow to your writing. First let's look at the coordinators you can use to join independent clauses. They are:

• For


• And


• Nor


• But


• Or


• Yet


• So"

Examples of compound sentences from softschools.com Link:

"

1. Sarah walked to class, but Kevin ran.




2. I want hamburgers, but Lois wants pizza.




3. The photographer held up a bear, and the little boy smiled.




4. I fell out of the bed, so Mom came to check on me.




5. The dog buried his bone, and the cat sniffed around it.




6. I was late; however, the class had not started.




7. I left my bag on the bus; therefore, I did not have a pencil.




8. Can I go home with you, so we can do our homework together?




9. It was very hot outside, and the ice cream melted.




10. Our team tried hard, but we lost the game."