TextSecure can access the following on your device:

Identity

• modify your own contact card
• find accounts on the device
• read your own contact card

Contacts

• modify your contacts
• read your contacts

SMS

• receive text messages (MMS)
• receive text messages (SMS)
• send SMS messages
• edit your text messages (SMS or MMS)
• read your text messages (SMS or MMS)

Phone

• read call log

Photos/Media/Files

• modify or delete the contents of your USB storage
• read the contents of your USB storage

Device ID & call information

• read phone status and identity

Other

• send WAP-PUSH-received broadcast
• receive data from Internet
• view network connections
• control vibration
• run at startup
• change network connectivity
• full network access
• prevent device from sleeping

--------------------------------------------------------

Last Update: 06/12/2015

Source:
https://play.google.com/store/apps/details?id=org.thoughtcrime.securesms