Yes, it is possible
plain text using a TI-83
There are currently two "products" on the market. The first, Encrypt, is a small program in the Texas Instruments archives. Its "encryption" consists of assigning conscutive numbers to the alphabetical characters, and then storing them all in a huge list. To decrypt, it just copies them back into a string. In essence, it acts as a simple transposition cipher, the method used by the Captain Midnight Decoder Ring, among others.
The second, Enc Pro v1.0b, is available at http://www.scruznet.com/~kibrick/ti/ (and was incidentally written by yours truly). Enc Pro uses a similar method to transpose the characters into a list, but then goes on to encode them and output a string of ciphertext. It provides 4 different algorithms that vary in security.
The first algorithm is a simple transposition cipher, similar to Caesar's Code, which simply shifts the encoding alphabet up a certain number of characters. Extremely low in security, probably not good enough to even fool siblings with, but a fun application for demonstrating simple encryption...
The second algorithm creates a cryptogram out of the plaintext. A cryptogram is another simple cipher, commonly used in sunday-paper puzzles, but will keep you guessing a little longer. Each encrypted letter is equivalent to a single alphabetic character. The goal of the puzzle is to use syntax and letter-frequency to match the encrypted letters with their real equivalents, and through that decipher the puzzle. Using this algorithm, you can either set the letter equivalency yourself, or calculate it automatically (a major time-saver!)
The third algorithm is harder to explain, but it uses a sequence of 4 numbers to shift the data in a binary algorithm. Since this cipher can include plaintext and output ciphertext for alphanumeric characters plus special symbols (including spaces), it appears quite a bit more formidable, and is much harder to crack.
The final algorithm creates a list of random transpositions, one for each character, and has similar capabilities to the previous cipher. However, without the original list of transforms, the encrypted data cannot be decrypted, because without knowing each individual transform, the data could be an infinite number of sentences. The algorithm can also export the lists themselves as ciphertext, encrypted with cipher 3, or stored as image files. A slightly less secure application lets you generate transforms from 10-digit numerical passwords.
While not as completely secure as PGP encryption, TI-83 Basic encryption can be transported anywhere, and can be used as an additional cipher if there is the possibiliy of another form of encryption being compromised. Considering that you can do encryption nearly as powerful as some high-level Pentagon ciphers on a standard graphing calculator, I can't wait to see what is possible with a TI-89...