Is this correct? Can we use a contraction here on the word picture?
A picture's worth a thousand words.
Yes and why would you? The apostrophe might cause confusion and definitely slows the reader down. Use the word "is".
'A picture's worth a thousand words' is how it would be said. If you're a non native speaker, it would be better for you to familiarise yourself with the contractions.
You'd only use them in informal English writing and, without doubt, you'd hear them used regularly on the street when natives are speaking.
Who says, ' A picture is worth a thousand words?' We put stress on the important words: picture, thousand and words. Words like A, The and of are rarely stressed.
Espero que te ayude