MetaMask for iOS by default doesn't show the Arbitrum network.
To add it manually, in Settings → Networks menu of the MetaMask app press 'Add Network', fill in the fields:
For Arbitrum mainnet (real money):
Network Name: Arbitrum
New RPC URL: https://arb1.arbitrum.io/rpc
Chain ID: 42161
Currency Symbol: AETH
Block Explorer URL: https://arbiscan.io/
For Arbitrum testnet (testing environment of the demo app):
Network Name: Arbitrum Rinkeby
New RPC URL: https://rinkeby.arbitrum.io/rpc
Chain ID: 421611
Currency Symbol: ARETH
Block Explorer URL: https://rinkeby-explorer.arbitrum.io/#/