Quote:
Originally Posted by BobRitter
¿Puedo acompañarte?  (Also: "¿Puedo acompañarla?", if you use "usted" instead of "tú")
¿Puedo juntarte?  (Be careful, this means "may I put you together?", as if she were in pieces to be gathered and be put into place.) 
¿Puedo unirte? (Same as the previous one.)
¿Puedo unirme a ustedes? (This is good for asking to join a group of people "unirse" to just one person sounds rather strange, unless you're getting married: "Nos unimos en matrimonio".
Grammatically speaking, you could use the verb like this: "¿Te me puedo unir?", but this sounds slightly creepy; it wouldn't be a good start for meeting someone. 
Also, notice how in the previous example, you used "unirte" and in the second one it was "unirme"; here, I am the "lose piece" who wants to join the group.) 
¿ Le (Although in Spain this is the usual pronoun, this is a direct object, so "la" is preferred.) puedo acompañar? (Also: "¿te puedo acompañar?", if you use "tú" instead of "usted")
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So, the most appropriate translation for "may I join you?", if you ask me, are both "¿puedo acompañarla/te?" and "¿la/te puedo acompañar?"
This is the same question, by the way, because the place of the pronoun doesn't change the meaning. Some of us prefer the pronoun closer to the main verb though: "¿puedo acompañarla/te?", because "puedo" is working as an auxiliary verb only, but most people are indifferent to where the pronoun is placed.