Safaricom shares can be purchased online via the Nairobi Securities Exchange (NSE) using any licensed stockbroker. The requirements of trading in shares are money, CDS account, bank account, kra pin and licensed stock broker.
Here is a list of licensed stock brokers by Capital Markets Authority (CMA): http://www.cmarcp.or.ke/index.php/licensee-accounts/stock-brokers
If you want to buy Safaricom shares online, make sure that you have selected a stock broker that offers online trading