Some points about making your code look more like idiomatic Ruby:

• Use nil.

    choice = -1
  

  should be

    choice = nil
  

• Don't wrap your conditional in brackets:

    while(choice != 3)
    if(choice == 1)
  

  should be

    while choice != 3
    if choice == 1
  

• Instead of initializing a variable to an empty array, use map to convert one array directly into the new form and use that to initialize your variable:

  Instead of this:

     #create empty hashes
     plain_alphabet  = {}
     cipher_alphabet = {} 
  
    "a".upto("z") {|x| plain_alphabet[x]  = ((x[0] - "a"[0]) % 26) }
    "A".upto("Z") {|x| cipher_alphabet[x] = ((x[0] - "A"[0]) % 26) }
  

  do this:

    plain_alphabet  = ("a".."z").map { |x| (x[0] - "a"[0]) % 26 }
    cipher_alphabet = ("A".."Z").map { |x| (x[0] - "A"[0]) % 26 }
  

  And instead of this:

    ciphertext = ""
  
    #fill in the ciphertext with mapping information in the caesar_map
    plaintext.split("").each do |c|
      ciphertext += $caesar_map[c]
    end
  

  do this:

    ciphertext = plaintext.split("").map { |c| $ceasar_map[c] }.join
  

Some points about making your code look more like idiomatic Ruby:

• Use nil.

    choice = -1
  

  should be

    choice = nil
  

• Don't wrap your conditional in brackets:

    while(choice != 3)
    if(choice == 1)
  

  should be

    while choice != 3
    if choice == 1
  

• Instead of initializing a variable to an empty array, use map to convert one array directly into the new form and use that to initialize your variable:

  Instead of this: Hashes != arrays, sorry. The principal still applies, even if this example isn't equivalent:

     #create empty hashes
     plain_alphabet  = {}
     cipher_alphabet = {} 
  
    "a".upto("z") {|x| plain_alphabet[x]  = ((x[0] - "a"[0]) % 26) }
    "A".upto("Z") {|x| cipher_alphabet[x] = ((x[0] - "A"[0]) % 26) }
  

  do this:

    plain_alphabet  = ("a".."z").map { |x| (x[0] - "a"[0]) % 26 }
    cipher_alphabet = ("A".."Z").map { |x| (x[0] - "A"[0]) % 26 }
  

  And instead of this:

    ciphertext = ""
  
    #fill in the ciphertext with mapping information in the caesar_map
    plaintext.split("").each do |c|
      ciphertext += $caesar_map[c]
    end
  

  do this:

    ciphertext = plaintext.split("").map { |c| $ceasar_map[c] }.join
  

• Use case when appropriate; rewrite your if/elsif/elsif/else as:

    case choice
    when 1:
      # ...
    when 2:
      # ...         
    when 3:
      # ...
    else
      # ...
    end
  

• Don't wrap your conditional in brackets:

    while(choice != 3)
    if(choice == 1)
  

  should be

    while choice != 3
    if choice == 1
  

• Use map to convert one array into another array; Instead of this,

    ciphertext = ""
  
    #fill in the ciphertext with mapping information in the caesar_map
    plaintext.split("").each do |c|
      ciphertext += $caesar_map[c]
    end
  

  do this:

    ciphertext = plaintext.split("").map { |c| $ceasar_map[c] }.join
  

Some points about making your code look more like idiomatic Ruby:

• Use nil.

    choice = -1
  

  should be

    choice = nil
  

• Don't wrap your conditional in brackets:

    while(choice != 3)
    if(choice == 1)
  

  should be

    while choice != 3
    if choice == 1
  

• Instead of initializing a variable to an empty array, use map to convert one array directly into the new form and use that to initialize your variable:

  Instead of this:

     #create empty hashes
     plain_alphabet  = {}
     cipher_alphabet = {} 
  
    "a".upto("z") {|x| plain_alphabet[x]  = ((x[0] - "a"[0]) % 26) }
    "A".upto("Z") {|x| cipher_alphabet[x] = ((x[0] - "A"[0]) % 26) }
  

  do this:

    plain_alphabet  = ("a".."z").map { |x| (x[0] - "a"[0]) % 26 }
    cipher_alphabet = ("A".."Z").map { |x| (x[0] - "A"[0]) % 26 }
  

  And instead of this:

    ciphertext = ""
  
    #fill in the ciphertext with mapping information in the caesar_map
    plaintext.split("").each do |c|
      ciphertext += $caesar_map[c]
    end
  

  do this:

    ciphertext = plaintext.split("").map { |c| $ceasar_map[c] }.join