Is it possible to use a Cisco 2950 switch as a DHCP relay?

You can do it. You need enhanced image on your switch for it to offer DHCP functionality. Use the following commands (available with Cisco 2950 documentation) for configuring the same:

Commands for DHCP functionality

configure terminal	To enter global configuration mode.
ip dhcp snooping	To enable DHCP snooping globally.
ip dhcp snooping vlan vlan-id [vlan-id]	To enable DHCP snooping on a VLAN or range of VLANs. You can specify a single VLAN identified by VLAN ID.
ip dhcp snooping information option	To enable the switch to insert and remove DHCP relay information (option-82 field) in forwarded DHCP request messages to the DHCP server. This is enabled by default.
interface [interface-id]	To enter interface configuration mode, and specify the interface to be configured.
ip dhcp snooping trust	This is an optional command. It configures the interface as trusted or un-trusted. The default is un-trusted.
ip dhcp snooping limit rate [rate]	This is an optional command. It configures the number of DHCP packets per second than an interface can receive. The range you can specify for [rate] is 1 to 4294967294. The default is no rate limit configured.

[ ] expects arguments to be given like VLAN-ID or rate limit. The first five commands should be enough to configure DHCP relay. The other two give the functionality more granularities.