No. You need a 3GS or later. See below:
See the chart below to determine whether you can upgrade your device and what you can upgrade to. If you do not have a Software Update option present on your iDevice, then you are trying to upgrade to iOS 5 or higher. You will have to connect your device to your computer and open iTunes in order to upgrade.
IPhone, iPod Touch, and iPad iOS Compatibility Chart
Device iOS Verson
iPhone 1 iOS 3.1.3
iPhone 3G iOS 4.2.1
iPhone 3GS iOS 6.1.x
iPhone 4 iOS 7.0.x
iPhone 4S iOS 7.0.x
iPhone 5 iOS 7.0.x
iPhone 5c iOS 7.0.x
iPhone 5s iOS 7.0.x
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iPod Touch 1 iOS 3.1.3
iPod Touch 2 iOS 4.2.1
iPod Touch 3 iOS 5.1.1
iPod Touch 4 iOS 6.1.x
iPod Touch 5 iOS 7.0.x
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iPad 1 iOS 5.1.1
iPad 2 iOS 7.0.x
iPad 3 iOS 7.0.x
iPad 4 iOS 7.0.x
iPad Mini iOS 7.0.x
iPad Air iOS 7.0.x
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Select the method most appropriate for your situation.
Upgrading iOS
1. How to update your iPhone, iPad, or iPod Touch
2. iPhone Support
3. iPod Touch Support
4. iPad Support
a. Updating Your iOS from iOS 5
Tap Settings > General > Software Update
If an update is available there will be an active Update button. If you are current,
then you will see a gray screen with a message saying your are up to date.
b. If you are still using iOS 4 — Updating your device to iOS 5 or later.
c. Resolving update problems
1. iOS - Unable to update or restore
2. iOS- Resolving update and restore alert messages
